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BEGIN:VEVENT
SUMMARY:Richard Kenyon (Yale University)
DTSTART:20210920T150000Z
DTEND:20210920T154500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/1
DESCRIPTION:Title: Multinomial models\nby Richard Kenyon (Yale University) as part o
f BIRS workshop: Permutations and Probability\n\n\nAbstract\nRandom tiling
models and other stat mech models like the Potts model\non a graph G beco
me tractable in a certain limit of “blow up”s G_N\,\nwhere each vertex
of G is replaced with N vertices and each edge with K_{N\,N}.\nWe give ex
act enumerations\, free energy\, phase transitions\, conformal invariance\
nproperties for these models. This is joint work with Cosmin Pohoata.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Ayyer (Indian Institute of Science)
DTSTART:20210920T161500Z
DTEND:20210920T170000Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/2
DESCRIPTION:Title: Toppleable permutations\, acyclic orientations and excedances\nby
Arvind Ayyer (Indian Institute of Science) as part of BIRS workshop: Perm
utations and Probability\n\n\nAbstract\nThe representation theory of the s
ymmetric group provides several\nbeautiful combinatorial formulas. The ide
a to use it to study random\nwalks comes from Diaconis and Shahshahani\, w
ho used some formulas to\nbound the eigenvalues of the random transpositio
n shuffle\, leading to a\ncutoff phenomenon.\nOur main goal will be to exp
lain how to improve their L^2 bound method\nto obtain cutoff profiles\, an
d more concretely how this applies to\nrandom transpositions.\n\nWe will f
irst recall some definitions and explain the link between\nrepresentation
theory and Fourier analysis. Then\, we will explain the\nlimit profile met
hod\, and its generalisation to reversible Markov chains\n(by Nestoridi an
d Olesker-Taylor). Finally\, we will discuss the\nMurnagham-Nakayama formu
la and its link with the fixed points of\npermutations.\n\nThe talk will n
ot assume prior knowledge of representation theory\, all\nrepresentation t
heoretic statements be also explained in terms of\neigenvalues and eigenve
ctors of the transition matrix.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louigi Addario-Berry (McGill University)
DTSTART:20210920T170000Z
DTEND:20210920T174500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/3
DESCRIPTION:Title: Height bounds for random trees\nby Louigi Addario-Berry (McGill U
niversity) as part of BIRS workshop: Permutations and Probability\n\n\nAbs
tract\nI will present new\, non-asymptotic bounds on the heights of random
combinatorial trees and conditioned Bienaymé trees\, as well as stochast
ic inequalities relating the heights of combinatorial trees with different
degree sequences. The tool for all the proofs is a new approach to coding
rooted trees by sequences.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Bordenave (Institut de Mathématiques de Marseille)
DTSTART:20210921T151500Z
DTEND:20210921T154500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/4
DESCRIPTION:by Charles Bordenave (Institut de Mathématiques de Marseille)
as part of BIRS workshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svante Linusson (KTH-Royal Institute of Technology Stockholm)
DTSTART:20210921T161500Z
DTEND:20210921T170000Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/5
DESCRIPTION:Title: Random walks in affine Weyl groups and TASEPs on signed permutations<
/a>\nby Svante Linusson (KTH-Royal Institute of Technology Stockholm) as p
art of BIRS workshop: Permutations and Probability\n\n\nAbstract\nWe study
random reduced walks in affine Weyl groups of types B\, C and D. These wa
lks almost surely approaches one of finitely many directions each correspo
nding to a signed permutation. We compute the exact directions for a natur
al set of parameters called Kac labels as weights for the walk. This settl
es a question by Thomas Lam\, for types B and C in the affirmative and for
type D in the negative. The main tool is a combinatorial two row model fo
r a totally asymmetric simple exclusion process called the D∗-TASEP\, wi
th four parameters. By specializing the parameters in different ways\, we
obtain TASEPs for each of the Weyl groups mentioned above\, i.e. on signed
permutations. Computing certain correlations in these TASEPs gives the de
sired limiting directions. We also state several explicit conjectures for
certain probabilities in these TASEPs on signed permutations.\nJoint work
with Erik Aas\, Arvind Ayyer and Samu Potka.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olya Mandelshtam (University of Waterloo)
DTSTART:20210921T170000Z
DTEND:20210921T174500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/6
DESCRIPTION:by Olya Mandelshtam (University of Waterloo) as part of BIRS w
orkshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gady Kozma (Weizmann Institute)
DTSTART:20210922T150000Z
DTEND:20210922T154500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/7
DESCRIPTION:Title: Mixing time\, quasi isometries and Cayley graphs\nby Gady Kozma (
Weizmann Institute) as part of BIRS workshop: Permutations and Probability
\n\n\nAbstract\nWe show that the (usual\, total variation) mixing time is
not a quasi-isometry invariant\, even between Cayley graphs. All terms wil
l be explained in the talk. Joint work with Jonathan Hermon.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Winkler (Dartmouth College)
DTSTART:20210922T161500Z
DTEND:20210922T170000Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/8
DESCRIPTION:Title: Permutons\nby Peter Winkler (Dartmouth College) as part of BIRS w
orkshop: Permutations and Probability\n\n\nAbstract\nWhat do large permuta
tions look like? We can in some cases answer this question with\nthe help
of limit structures called "permutons\," and a variational principle.\n
Examples show nice apparent behavior and some contrasts to the case of gr
aphs and graphons.\nJoint work with Rick Kenyon\, Dan Kral' and Charles Ra
din\; later\, with Chris Coscia\, Sayan Das\,\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Bouvel (CNRS)
DTSTART:20210923T150000Z
DTEND:20210923T154500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/9
DESCRIPTION:Title: Random permutations biased according to their records\nby Mathild
e Bouvel (CNRS) as part of BIRS workshop: Permutations and Probability\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svante Janso (Uppsala University)
DTSTART:20210923T161500Z
DTEND:20210923T170000Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/10
DESCRIPTION:Title: The number of occurrences of patterns and constrained patterns in a
random permutation\nby Svante Janso (Uppsala University) as part of BI
RS workshop: Permutations and Probability\n\n\nAbstract\nA pattern $\\tau$
is a fixed (short) permutation. We are interested in the\nnumber of occur
rences of a pattern $\\tau$ in a random (long) permutation\n$\\pi$\, where
an occurrence is a subsequence with the same relative order as\n$\\tau$.
We also consider constrained cases\, where we count only occurrences\nwith
some restrictions on the gaps between the elements of the subsequence.\nI
n particular\, we consider vincular patterns\, where some elements in the\
nsubsequence are required to be adjacent in $\\pi$.\n\nAsymptotic normalit
y has been shown by Bóna (2007\, 2008\, 2010) and (vincular permutations)
Hofer (2018). We show that these results follow from\ngeneral results on
U-statistics. For constrained (e.g. vincular) cases\, this\nrequires resul
ts on m-dependent U-statistics.\n\nWe consider also linear combinations of
counts for several patterns.\nTypically\, these too are asymptotically no
rmal\, but there are degenerate\ncases\, see Janson\, Nakamura and Zeilber
ger (2015) and Even-Zohar (2020).\nMuch is known about degenerate cases to
o\, but there are also open problems\,\nin particular for constrained case
s.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Teyssier (Universität Wien)
DTSTART:20210924T150000Z
DTEND:20210924T154500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/11
DESCRIPTION:Title: Cutoff profile for random transpositions\nby Lucas Teyssier (Uni
versität Wien) as part of BIRS workshop: Permutations and Probability\n\n
\nAbstract\nThe representation theory of the symmetric group provides seve
ral beautiful combinatorial formulas. The idea to use it to study random w
alks comes from Diaconis and Shahshahani\, who used some formulas to bound
the eigenvalues of the random transposition shuffle\, leading to a cutoff
phenomenon. Our main goal will be to explain how to improve their L^2 bou
nd method to obtain cutoff profiles\, and more concretely how this applies
to random transpositions.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Holroyd (University of Bristol)
DTSTART:20210924T161500Z
DTEND:20210924T170000Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/12
DESCRIPTION:by Alexander Holroyd (University of Bristol) as part of BIRS w
orkshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Williams (Harvard University)
DTSTART:20210924T170000Z
DTEND:20210924T174500Z
DTSTAMP:20260422T185417Z
UID:BIRS-21w5511/13
DESCRIPTION:Title: Schubert polynomials\, the inhomogeneous TASEP\, and evil-avoiding p
ermutations\nby Lauren Williams (Harvard University) as part of BIRS w
orkshop: Permutations and Probability\n\n\nAbstract\nThe totally asymmetri
c simple exclusion process (TASEP) was introduced around 1970 as a model f
or translation in protein synthesis and traffic flow. The inhomogeneous TA
SEP is a Markov chain of weighted particles hopping on a lattice\, in whic
h the hopping rate depends on the weight of the particles being interchang
ed. We will consider the case where the lattice is a ring\, and each parti
cle has a distinct weight\, so that we can think of this model as a Markov
chain on permutations. We will see that in many cases\, and in particular
for w an "evil-avoiding" permutation\, the steady state probability of w
can be expressed in terms of Schubert polynomials. Based on joint work wit
h Donghyun Kim. The inhomogeneous TASEP\, Schubert polynomials\, and evil-
avoiding permutations\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5511/13/
END:VEVENT
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