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BEGIN:VEVENT
SUMMARY:Wojciech Niemiro (University of Warsaw)
DTSTART:20200515T081500Z
DTEND:20200515T093000Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/1
DESCRIPTION:Title: Estimation of the growth rate for Lévy processes with boun
ded positive jumps\nby Wojciech Niemiro (University of Warsaw) as part
of Theory of Markov Semigroups and Schrödinger Operators\n\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshihiro Uemura (Kansai University)
DTSTART:20200522T081500Z
DTEND:20200522T093000Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/2
DESCRIPTION:Title: On symmetric stable-type processes with singular/degenerate
coefficitents\nby Toshihiro Uemura (Kansai University) as part of The
ory of Markov Semigroups and Schrödinger Operators\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateusz Kwaśnicki (Wrocław University of Science and Technology)
DTSTART:20200529T081500Z
DTEND:20200529T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/3
DESCRIPTION:Title: Spectral theory for non-symmetric Lévy processes in the ha
lf-line\nby Mateusz Kwaśnicki (Wrocław University of Science and Tec
hnology) as part of Theory of Markov Semigroups and Schrödinger Operators
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Swart (Czech Academy of Sciences)
DTSTART:20201009T081500Z
DTEND:20201009T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/4
DESCRIPTION:Title: Recursive tree processes and the mean-field limit of stocha
stic flows\nby Jan Swart (Czech Academy of Sciences) as part of Theory
of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nInteractin
g particle systems can often be constructed from a graphical representatio
n\, by applying local maps at the times of associated Poisson processes. T
his leads to a natural coupling of systems started in different initial st
ates. In the talk\, we will look at interacting particle systems on the co
mplete graph in the mean-field limit\, i.e.\, as the number of vertices te
nds to infinity. We will not only be interested in the mean-field limit of
a single process\, but mainly in how several coupled processes behave in
the limit. In particular\, we want to know how sensitive the Poisson const
ruction is to small changes in the initial state. This turns out to be clo
sely related to recursive tree processes as studied by Aldous and Bandyopa
dyay\, which are a sort of Markov chains in which time has a tree-like str
ucture and in which the state of each vertex is a random function of its d
escendants. The abstract theory will be demonstrated on an example of a pa
rticle system with cooperative branching and deaths.\n\nThis is joint work
with Anja Sturm and Tibor Mach.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew J. Jurek (University of Wroclaw)
DTSTART:20201016T081500Z
DTEND:20201016T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/5
DESCRIPTION:Title: Compositions of some random integral mappings (and a conjec
ture)\nby Zbigniew J. Jurek (University of Wroclaw) as part of Theory
of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nIn the 1980
s\, Lévy class L of selfdecomposable distributions was characterized as d
istributions of some homomorphisms between convolution subsemigroups of ID
(the semigroup of all infinitely divisible measures). We will show that c
ompositions of those random integrals (mappings) can be always expressed a
s another single random integral mapping. That fact is illustrated by some
old Thorin class T. Finally\, we will discuss a conjecture that (some) cl
asses of limit laws always admit random integral representations.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Perkowski (Free University of Berlin)
DTSTART:20201023T081500Z
DTEND:20201023T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/6
DESCRIPTION:Title: Mass asymptotics for the 2d parabolic Anderson model with w
hite noise potential\nby Nicolas Perkowski (Free University of Berlin)
as part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAb
stract\nWe study the long time behavior of the total mass of the 2d parabo
lic Anderson model (PAM) with white noise potential\, which is the univers
al scaling limit of 2d branching random walks in small random environments
. There are several known results on the long time behavior of the PAM for
more regular potentials\, but the 2d white noise is very singular and it
requires renormalization techniques. In particular\, the Feynman–Kac rep
resentation\, usually the main tool for deriving asymptotics\, breaks down
. To overcome this problem we use a measure transform and we introduce a n
ew “partial Feynman–Kac representation”. The new representation is b
ased on a diffusion with distributional drift\, and we derive Gaussian hea
t kernel bounds for such diffusions. \n\nBased on joint works with Wolfgan
g König and Willem van Zuijlen.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Workshop (TU Dresden & Wroclaw University of Technology)
DTSTART:20201026T140000Z
DTEND:20201026T164500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/7
DESCRIPTION:Title: Nonlocal Operators and Markov Processes\, Oct 26–30\, 202
0\nby Workshop (TU Dresden & Wroclaw University of Technology) as part
of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\n
Format: open Zoom webinar\n\nRegistration and details: http://prac.im.pwr.
wroc.pl/~bogdan/nomp.html\n\nSchedule (all times given in Wroclaw Dresden
time=GMT+2h):\n\n\nMonday\, 26 Oct:\n\n15:00-15:45 and 16:00-16:45 Xavier
Ros-Oton\, Boundary regularity for nonlocal operators 1\n\n17:00-17:45 Fra
nziska Kühne\, Lévy-type processes 1\n\n\nTuesday\, 27 Oct:\n\n15:00-15:
45 and 16:00-16:45 Xavier Ros-Oton\, Boundary regularity for nonlocal oper
ators 2\n\n17:00-17:45 Franziska Kühne\, Lévy-type processes 2\n\nWednes
day\, 28 Oct:\n\n\n15:00-15:45 and 16:00-16:45 Xavier Ros-Oton\, Boundary
regularity for nonlocal operators 3\n\n17:00-17:45 Mateusz Kwaśnicki\, Po
tential theory of Markov processes 1\n\nThursday\, 29 Oct:\n\n\n15:00-15:4
5 and 16:00-16:45 Xavier Ros-Oton\, Boundary regularity for nonlocal opera
tors 4\n\n17:00-17:45 Mateusz Kwaśnicki\, Potential theory of Markov proc
esses 2\n\n\nFriday\, 30 Oct (note different hour):\n\nRecent Topics and D
evelopments:\n\n10:15-11:00 Enrico Valdinoci\, The Bernstein technique for
integrodifferential equations\n\n11:15-12:00 Bartłomiej Dyda\, On fracti
onal Hardy inequalities\n\n12:15-13:00 Alex Kulik\, Parametrix technique f
or complicated Lévy-type models\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Burdzy (University of Washington)
DTSTART:20201112T171500Z
DTEND:20201112T181500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/8
DESCRIPTION:Title: Fleming–Viot processes and $X=AX+B$ equation\nby Krzy
sztof Burdzy (University of Washington) as part of Theory of Markov Semigr
oups and Schrödinger Operators\n\n\nAbstract\nI will start with a review
of Fleming–Viot processes. I will state two open problems and some parti
al results. A specific Fleming–Viot model was an inspiration for a Law o
f Iterated Logarithm-type result. This result has a rather limited signifi
cance. The method of proof\, we hope\, may have an independent interest.\n
\n\nJoint work with Bartosz Kołodziejek and Tvrtko Tadić.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yehuda Pinchover (Technion – Israel Institute of Technology)
DTSTART:20201211T091500Z
DTEND:20201211T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/9
DESCRIPTION:Title: On families of optimal Hardy-weights for linear second-orde
r elliptic operators\nby Yehuda Pinchover (Technion – Israel Institu
te of Technology) as part of Theory of Markov Semigroups and Schrödinger
Operators\n\n\nAbstract\nWe construct families of optimal Hardy-weights fo
r a subcritical linear second-order elliptic operator using a one-dimensio
nal reduction. More precisely\, we first characterize all optimal Hardy-we
ights with respect to one-dimensional subcritical Sturm-Liouville operator
s on $(a\,b)$\, $\\infty \\leq a < b \\leq \\infty$\, and then apply this
result to obtain families of optimal Hardy inequalities for general linear
second-order elliptic operators in higher dimensions. This is a joint wor
k with Idan Versano.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:René Schilling (Technische Universität Dresden)
DTSTART:20210115T091500Z
DTEND:20210115T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/10
DESCRIPTION:Title: Some Remarks on the Liouville Theorem for Generators of L
évy Processes\nby René Schilling (Technische Universität Dresden) a
s part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbst
ract\nWe discuss various proofs of the (strong) Liouville property for non
-local operators.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Geiss (University of Jyväskylä)
DTSTART:20201120T091500Z
DTEND:20201120T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/11
DESCRIPTION:Title: On Riemann–Liouville operators\, BMO\, and gradient esti
mates in the Lévy–Itô space\nby Stefan Geiss (University of Jyväs
kylä) as part of Theory of Markov Semigroups and Schrödinger Operators\n
\n\nAbstract\nWe discuss in a stochastic framework the interplay between R
iemann–Liouville operators applied to càdlàg processes\, real interpol
ation\, bounded mean oscillation\, and estimates for gradient processes on
the Lévy–Itô space. We prove upper and lower bounds for these gradien
t processes\, where we are concerned with Hilbert space valued gradients a
nd where its regularity depends on the direction within the Hilbert space.
It turns out that certain Hölder properties of the terminal functions tr
ansfer into a singularity in time that can be compensated by Riemann–Lio
uville operators.\n\nThe talk is based on the preprint:\n\n S. Geiss\,
T.T. Nguyen: On Riemann–Liouville operators\, BMO\, gradient estimates i
n the Lévy–Itô space\, and approximation\, arXiv:2009.00899.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain-Sol Sznitman (ETH Zürich)
DTSTART:20210319T091500Z
DTEND:20210319T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/12
DESCRIPTION:Title: Excess deviations for points disconnected by random interl
acements\nby Alain-Sol Sznitman (ETH Zürich) as part of Theory of Mar
kov Semigroups and Schrödinger Operators\n\n\nAbstract\nThe study of larg
e deviation events involving disconnection by random interlacements or of
similar large deviation events for the closely related model of level-set
percolation of the Gaussian free field has been an active subject of resea
rch in the last years.\nIn this talk we describe a recent result concernin
g random interlacements on Z^d\, d≥3\, in the strongly percolative regim
e. Given a large box centered at the origin we investigate the exponential
rate of decay of the probability that the box contains an excessive fract
ion of points that are disconnected by random interlacements from the boun
dary of a box of double size.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dariusz Buraczewski (University of Wrocław)
DTSTART:20201127T091500Z
DTEND:20201127T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/13
DESCRIPTION:Title: On the branching random walk and the derivative martingale
\nby Dariusz Buraczewski (University of Wrocław) as part of Theory of
Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nWe will descr
ibe the branching random walk (BRW) and its fundamental properties includi
ng the central limit theorem. A crucial role in analyzing the BRW is playe
d by the so-called derivative martingale. We will discuss new results conc
erning the derivative martingale. The talk is based on a joint work with A
leksander Iksanov and Bastien Mallein.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Hairer (Imperial College London)
DTSTART:20201218T091500Z
DTEND:20201218T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/14
DESCRIPTION:Title: Averaging of non-Markovian SDEs\nby Martin Hairer (Imp
erial College London) as part of Theory of Markov Semigroups and Schrödin
ger Operators\n\n\nAbstract\nWe consider slow / fast systems where the slo
w system is driven by fractional Brownian motion with Hurst parameter $H >
1/2$. We show that unlike in the case $H=1/2$\, convergence to the averag
ed solution takes place in probability and the limiting process solves the
“naively” averaged equation. Our proof strongly relies on the recentl
y obtained stochastic sewing lemma.\n\nJoint with Xue-Mei Li.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damir Kinzebulatov (Laval University)
DTSTART:20201204T110000Z
DTEND:20201204T120000Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/15
DESCRIPTION:Title: Fractional Kolmogorov operator and desingularizing weights
\nby Damir Kinzebulatov (Laval University) as part of Theory of Markov
Semigroups and Schrödinger Operators\n\n\nAbstract\nWe establish sharp t
wo-sided bounds on the heat kernel of the fractional Laplacian perturbed b
y Hardy-type drift by transferring it to an appropriate weighted space wit
h singular weight. The talk is based on joint papers with Yu.A.Semenov and
K.Szczypkowski.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Szczypkowski (Wrocław University of Science and Technology)
DTSTART:20201106T091500Z
DTEND:20201106T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/16
DESCRIPTION:Title: Non-symmetric Lévy processes\nby Karol Szczypkowski (
Wrocław University of Science and Technology) as part of Theory of Markov
Semigroups and Schrödinger Operators\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Toniazzi (University of Otago)
DTSTART:20210129T091500Z
DTEND:20210129T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/18
DESCRIPTION:Title: Censored stable subordinators and relaxation\nby Loren
zo Toniazzi (University of Otago) as part of Theory of Markov Semigroups a
nd Schrödinger Operators\n\n\nAbstract\nMotivated by popular models of no
n-exponential relaxation based on stable subordinators\, we consider a sta
ble subordinator censored when jumping above a barrier. We show this proce
ss hits the barrier in a finite time\, whose Laplace transform solves the
‘censored’ relaxation equation. This solution turns out to be a comple
tely monotone series\, modeling algebraic decay of order between 1 and 2\;
decay unattainable by comparable models. We also discuss how we identifie
d a new sub-diffusion process and several unanswered questions.\n\nJoint w
ork with Qiang Du and Zirui Xu (arXiv:1906.07296).\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radosław Adamczak (University of Warsaw)
DTSTART:20210122T091500Z
DTEND:20210122T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/19
DESCRIPTION:Title: Modified log-Sobolev inequalities\, Beckner inequalities a
nd moment estimates\nby Radosław Adamczak (University of Warsaw) as p
art of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstrac
t\nI will present recent results concerning the equivalence between the mo
dified log-Sobolev inequality and a family of Beckner type inequalities wi
th constants uniformly separated from zero. Next I will discuss moment est
imates which can be derived from such inequalities\, generalizing previous
results due to Aida and Stroock\, based on a stronger log-Sobolev inequal
ity due to Federbush and Gross. If time permits I will present examples to
moment estimates for certain Cauchy type measures\, for invariant measure
s of Glauber dynamics and on the Poisson path space.\n\nBased on joint wor
k with B. Polaczyk and M. Strzelecki.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daesung Kim (Uniwersytet Illinois at Urbana-Champaign)
DTSTART:20210305T130000Z
DTEND:20210305T140000Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/20
DESCRIPTION:Title: Hardy–Stein identity and Fourier multipliers\nby Dae
sung Kim (Uniwersytet Illinois at Urbana-Champaign) as part of Theory of M
arkov Semigroups and Schrödinger Operators\n\n\nAbstract\nThe classical H
ardy-Stein identity gives a representation of the $L^p$ norm of a function
in terms of a semigroup associated with Brownian motion. The identity was
used to derive the $L^p$ boundedness of the Littlewood-Paley square funct
ions\, which leads to that of Fourier multiplier operators. In this talk\,
we discuss the extension of the Hardy-Stein identity to non-symmetric pur
e jump Levy processes and a certain class of martingales. The proof is bas
ed on the Ito's formula for a general stochastic process.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew Palmowski (Wrocław University of Science and Technology)
DTSTART:20210312T091500Z
DTEND:20210312T101500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/21
DESCRIPTION:Title: On the renewal theorem for maxima on trees\nby Zbignie
w Palmowski (Wrocław University of Science and Technology) as part of The
ory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nWe cons
ider the distributional fixed-point equation: \\[R \\stackrel{\\mathcal{D}
}{=} Q \\vee \\left( \\bigvee_{i=1}^N C_i R_i \\right)\,\\] where the $R_i
$ are i.i.d. copies of $R$\, independent of the vector $(Q\, N\, \\{C_i\\}
)$\, with $N \\in \\mathbb{N}$\, $Q\, C_i \\geq 0$ and $P(Q > 0) > 0$. By
setting $W = \\log R$\, $X_i = \\log C_i$\, $Y = \\log Q$ it is equivalent
to the high-order Lindley equation \\[W \\stackrel{\\mathcal{D}}{=} \\max
\\left\\{ Y\, \\\, \\max_{1 \\leq i \\leq N}(X_i + W_i) \\right\\}.\\] It
is known that under Kesten assumptions\,\\[P(W > t) \\sim H e^{-\\alpha t}
\, \\qquad t \\to \\infty\,\\]where $\\alpha>0$ solves the Cramér--Lundbe
rg equation $E \\left[ \\sum_{j=1}^N C_i^\\alpha \\right] = E\\left[ \\sum
_{i=1}^N e^{\\alpha X_i} \\right] = 1$. The main goal of this paper is to
provide an explicit representation for $P(W > t)$\, which can be directly
connected to the underlying weighted branching process where $W$ is constr
ucted and that can be used to construct unbiased and strongly efficient es
timators for all $t$. Furthermore\, we show how this new representation ca
n be directly analyzed using Alsmeyer's Markov renewal theorem\, yielding
an alternative representation for the constant $H$. We provide numerical e
xamples illustrating the use of this new algorithm.\n\nThis is a joint wor
k with Bojan Basrak\, Michael Conroy and Mariana Olvera-Cravioto (arXiv:20
04.08966).\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Workshop (TU Dresden & Wrocław University of Science and Technolo
gy)
DTSTART:20210322T090000Z
DTEND:20210322T140000Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/22
DESCRIPTION:Title: Nonlocal Operators and Markov Processes II workshop\, Mar
22–26\, 2021\nby Workshop (TU Dresden & Wrocław University of Scien
ce and Technology) as part of Theory of Markov Semigroups and Schrödinger
Operators\n\n\nAbstract\nFormat: Virtual Zoom Conference\n\nRegistration
and details: http://prac.im.pwr.wroc.pl/~bogdan/nomp-II.html\n\nSchedule:\
n\n(times are given in Wroclaw-Dresden time -- GMT+1h)\n\n\nMonday\, 22 Ma
r:\n\n10:00-11:00 Alex Kulik\n\n11:00-12:00 Reinhard Höpfner\n\n14:00-15:
00 René Schilling\n\n\nTuesday\, 23 Mar:\n\n10:00-11:00 Reinhard Höpfner
\n\n11:00-12:00 Alex Kulik\n\n14:00-15:00 Noufel Frikha\n\n\nWednesday\, 2
4 Mar:\n\n10:00-11:00 Arturo Kohatsu-Higa\n\n11:00-12:00 Arnaud Gloter\n\n
14:00-15:00 Reinhard Höpfner\n\n\n\nThursday\, 25 Mar:\n\n10:00-11:00 And
rea Pascucci\n\n11:00-12:00 Arturo Kohatsu-Higa\n\n14:00-15:00 Arnaud Glot
er \n\n\n\nFriday\, 26 Mar:\n\n10:00-11:00 Arnaud Gloter\n\n11:00-12:00 Al
ex Kulik\n\n14:00-15:00 Arturo Kohatsu-Higa\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zbigniew Palmowski (Wrocław University of Science and Technology)
DTSTART:20210423T081500Z
DTEND:20210423T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/23
DESCRIPTION:Title: Extreme positions of regularly varying branching random wa
lk in random environment\nby Zbigniew Palmowski (Wrocław University o
f Science and Technology) as part of Theory of Markov Semigroups and Schr
ödinger Operators\n\n\nAbstract\nIn this talk\, we consider a Branching R
andom Walk (BRW) on the real line where the underlying genealogical struct
ure is given through a supercritical branching process in i.i.d. environme
nt and satisfies Kesten–Stigum condition. The displacements coming from
the same parent are assumed to have jointly regularly varying tails. Condi
tioned on the survival of the underlying genealogical tree\, we prove that
the appropriately normalized (depends on the expected size of the nth gen
eration given the environment) maximum among positions at the nth generati
on converges weakly to a scale-mixture of Frechét random variable. Furthe
rmore\, we derive the weak limit of the extremal processes composed of app
ropriately scaled positions at the nth generation and show that the limit
point process is a member of the randomly scaled scale-decorated Poisson p
oint processes (SScDPPP). Hence\, an analog of the predictions by Brunet a
nd Derrida (2011) holds.\n\nThis is a joint work with Ayan Bhattacharya (a
rXiv:2101.05369).\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Lenczewska (Wrocław University of Science and Technology)
DTSTART:20210409T081500Z
DTEND:20210409T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/24
DESCRIPTION:Title: Optimal Hardy inequality for the fractional Laplacian on L
^p\nby Julia Lenczewska (Wrocław University of Science and Technology
) as part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nA
bstract\nWe give an optimal Hardy inequality for a generalization of the q
uadratic form\, the Sobolev–Bregman form\, of the fractional Laplacian o
n $L^p(\\mathbb R^d)$. We present an application of our results to the con
tractivity of the Feynman–Kac semigroup $\\tilde P_t$\ngenerated by $\\D
elta^{\\alpha/2}+\\kappa |x|^{-\\alpha}$. The talk is based on a joint wor
k with Krzysztof Bogdan\, Tomasz Jakubowski and Katarzyna Pietruska-Pałub
a\, available at arXiv:2103.06550.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Longmin Wang (Nankai University)
DTSTART:20210416T081500Z
DTEND:20210416T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/25
DESCRIPTION:Title: Isotropic alpha-self-similar Markov process with a skew-pr
oduct structure\nby Longmin Wang (Nankai University) as part of Theory
of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\nLet $\\tau
_C$\nbe the exit time from a cone $C$ of an isotropic $\\alpha$-self-simil
ar Markov process $X_t$\nwith a skew-product structure\, that is $X_t$\nis
a product of its radial process and independent time changed angular comp
onent $\\Theta_t$\n. Under some additional regularity assumptions\, we pro
ve that\n$$\n\\mathbb P_x(\\tau_C >t) \\approx h(x) t^{-\\kappa_1}\n$$\nas
$t \\to \\infty$ for $h$ and $\\kappa_1$\nidentified explicitly. This is
a joint work with Zbigniew Palmowski.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Pascucci (Alma Mater Studiorum – Università di Bologna)
DTSTART:20210430T081500Z
DTEND:20210430T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/26
DESCRIPTION:Title: On stochastic Langevin and Fokker-Planck equations\nby
Andrea Pascucci (Alma Mater Studiorum – Università di Bologna) as part
of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbstract\n
We study existence\, regularity in Hölder classes and estimates from abov
e and below of the fundamental solution of a degenerate (S)PDE satisfying
the weak Hörmander condition. We discuss different notions of intrinsic r
egularity. We apply a Wentzell’s formula to reduce the SPDE to a PDE wit
h random coefficients to which we apply the parametrix technique and const
ruct a fundamental solution.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Małecki (Wrocław University of Science and Technology)
DTSTART:20210514T081500Z
DTEND:20210514T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/27
DESCRIPTION:Title: Archimedes principle for ideal gas\nby Jacek Małecki
(Wrocław University of Science and Technology) as part of Theory of Marko
v Semigroups and Schrödinger Operators\n\n\nAbstract\nWe prove Archimedes
’ principle for a macroscopic ball in ideal gas consisting of point part
icles with non-zero mass. The main result is an asymptotic theorem\, as th
e number of point particles goes to infinity and their total mass remains
constant. We also show that\, asymptotically\, the gas has an exponential
density as a function of height. We find the asymptotic inverse temperatur
e of the gas. We derive an accurate estimate of the volume of the phase sp
ace using the local central limit theorem. The talk is based on a joint wo
rk with Krzysztof Burdzy.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Komorowski (Institute of Mathematics of the Polish Academy
of Sciences)
DTSTART:20210618T081500Z
DTEND:20210618T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/28
DESCRIPTION:Title: Diffusive and superdiffusive limits for a kinetic equation
with a boundary condition\nby Tomasz Komorowski (Institute of Mathema
tics of the Polish Academy of Sciences) as part of Theory of Markov Semigr
oups and Schrödinger Operators\n\n\nAbstract\nWe consider the limit of a
linear kinetic equation\, with reflection-transmission-absorption at a poi
nt interface. The scattering kernel is degenerate. The equation arises fro
m a microscopic chain of oscillators in contact with a heat bath. In the a
bsence of the interface\, the solutions exhibit either diffusive\, or supe
rdiffusive behavior in the long time limit\, depending on whether the disp
ersion relation for the chain is optical\, or acoustic. The latter corresp
onds to either the presence\, or absence of an external potential acting o
n the chain. With the interface\, the long time limit is either the unique
solution of a heat equation with a Dirichlet boundary condition (in the o
ptical case)\, or a version of the fractional in space heat equation\, wit
h reflection-transmission-absorption at the interface (in the acoustic cas
e). In the latter case the limit problem corresponds to a certain stable p
rocess that is either absorbed\, reflected\, or transmitted upon crossing
the interface. The results have been obtained in collaboration with G. Bas
ile (Univ. Roma I)\, S. Olla (Univ. Paris-Dauphine)\, L. Ryzhik (Stanford
Univ.) and H. Spohn (TU München).\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conference
DTSTART:20210524T081500Z
DTEND:20210524T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/29
DESCRIPTION:Title: Probability and Analysis 2021 online conference\, May 24
–28\, 2021\nby Conference as part of Theory of Markov Semigroups and
Schrödinger Operators\n\n\nAbstract\nFormat: online conference (open Zoo
m webinar -- registration required)\n\nRegistration and program: http://pa
2021.im.pwr.edu.pl/\n\nPlease note that all times in the schedule are give
n in Wroclaw (Poland) time=GMT+2h.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Leżaj (Wrocław University of Science and Technology)
DTSTART:20210611T081500Z
DTEND:20210611T091500Z
DTSTAMP:20260404T085020Z
UID:MarkovProcessesWroclaw/30
DESCRIPTION:Title: Transition densities of spectrally positive Lévy processe
s\nby Łukasz Leżaj (Wrocław University of Science and Technology) a
s part of Theory of Markov Semigroups and Schrödinger Operators\n\n\nAbst
ract\nWe prove asymptotic behaviour of transition densities for a large cl
ass of spectrally one-sided Lévy processes of unbounded variation satisfy
ing mild condition imposed on the second derivative of the Laplace exponen
t\, or equivalently\, on the real part of the characteristic exponent. We
also provide sharp two-sided estimates on the density when restricted addi
tionally to processes without Gaussian component.\n
LOCATION:https://researchseminars.org/talk/MarkovProcessesWroclaw/30/
END:VEVENT
END:VCALENDAR