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SUMMARY:Ron Peled (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200915T153000Z
DTEND;VALUE=DATE-TIME:20200915T161000Z
DTSTAMP;VALUE=DATE-TIME:20240328T232622Z
UID:BIRS_20w5203/1
DESCRIPTION:Title: Euclidean random permutations\nby Ron Peled (Tel Aviv University)
as part of BIRS workshop: Permutations and Probability\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5203/1/
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SUMMARY:Evita Nestoridi (Princeton University)
DTSTART;VALUE=DATE-TIME:20200915T161500Z
DTEND;VALUE=DATE-TIME:20200915T165500Z
DTSTAMP;VALUE=DATE-TIME:20240328T232622Z
UID:BIRS_20w5203/2
DESCRIPTION:Title: Mixing results for the interchange and exclusion processes with open
boundaries\nby Evita Nestoridi (Princeton University) as part of BIRS
workshop: Permutations and Probability\n\n\nAbstract\nAssign district card
s to the vertices of a finite\, connected graph G(V\, E) with |V|=n. The i
nterchange process is a card shuffling scheme generated by flipping the ca
rds at the ends of the edges of the graph. The exclusion process follows t
he same dynamics where instead each vertex is assigned one of two colors.
In this talk\, I will discuss recent developments concerning the mixing ti
me of these two processes on the interval of length n. I will focus in par
ticular on the asymmetric exclusion process with open boundaries\, where p
articles are allowed to jump in and out from the ends of the interval. Thi
s is joint work with Gantert and Schmid.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5203/2/
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SUMMARY:Duncan Dauvergne (Princeton University)
DTSTART;VALUE=DATE-TIME:20200917T153000Z
DTEND;VALUE=DATE-TIME:20200917T161000Z
DTSTAMP;VALUE=DATE-TIME:20240328T232622Z
UID:BIRS_20w5203/3
DESCRIPTION:Title: The scaling limit of the longest increasing subsequence\nby Dunca
n Dauvergne (Princeton University) as part of BIRS workshop: Permutations
and Probability\n\n\nAbstract\nI will describe a framework for proving con
vergence to the directed landscape\, the central limit object in the KPZ u
niversality class. The directed landscape is a random scale-invariant `dir
ected' metric on the plane. One highlight of this work is that the scaling
limit of the longest increasing subsequence in a uniformly random permuta
tion is a geodesic in the directed landscape. Joint work with Balint Virag
.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5203/3/
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SUMMARY:Mickaël Maazoun (Oxford University)
DTSTART;VALUE=DATE-TIME:20200917T161500Z
DTEND;VALUE=DATE-TIME:20200917T165500Z
DTSTAMP;VALUE=DATE-TIME:20240328T232622Z
UID:BIRS_20w5203/4
DESCRIPTION:Title: Scaling limits of Baxter permutations and bipolar orientations\nb
y Mickaël Maazoun (Oxford University) as part of BIRS workshop: Permutati
ons and Probability\n\n\nAbstract\nJoint work with Jacopo Borga\, https://
arxiv.org/abs/2008.09086 .\n\nThe theory of permutons allows us to express
scaling limits of the diagram of permutations. Scaling limits of uniform
elements in various classes of pattern-avoiding permutations have attracte
d a fair amount of attention lately. We show such a result for Baxter perm
utations\, a famous class of permutations avoiding generalized patterns.\n
\nA remarkable bijection of Bousquet-Mélou\, Bonichon and Fusy (2010) wit
h bipolar orientations\, a type of decorated planar maps\, allows us to ex
press a Baxter permutation in terms of the relationship between the mating
-of-trees encoding (Kenyon\, Miller\, Sheffield\, Wilson\, 2015) of a bipo
lar orientation and the one of its dual map. This was already studied by G
wynne\, Holden\, Sun (2016)\, and our main result can be seen as an improv
ement of theirs.\n\nThe main step of our approach is to encode the problem
in a "coalescent-walk" process\, which converges to the coalescing proces
s obtained when solving the perturbed Tanaka SDE (Prokaj\, 2011) with the
same Brownian noise at different starting times. If time allows\, I will t
alk about the robustness of the method and possible generalizations.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5203/4/
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BEGIN:VEVENT
SUMMARY:Dan Romik (University of California Davis)
DTSTART;VALUE=DATE-TIME:20200917T170000Z
DTEND;VALUE=DATE-TIME:20200917T174000Z
DTSTAMP;VALUE=DATE-TIME:20240328T232622Z
UID:BIRS_20w5203/5
DESCRIPTION:Title: Distributional identities and absorbing time asymptotics in the orien
ted swap process\nby Dan Romik (University of California Davis) as par
t of BIRS workshop: Permutations and Probability\n\n\nAbstract\nThe orient
ed swap process is a model for a random sorting network\, in which N parti
cles labeled 1\,...\,N arranged on the discrete lattice [1\,N] start out i
n increasing order and then perform successive adjacent swaps at random ti
mes until they reach the reverse configuration N\,...\,1. An open problem
from 2009 asked for the limiting law of the absorbing time of the process.
In recent joint works with Bisi-Cunden-Gibbons and Bufetov-Gorin\, we res
olved this problem by showing that the limiting law is the Tracy-Widom GOE
distribution\, aka F_1. I will tell the story of this result and how it c
ame to be discovered and proved\, which involves connections to recent wor
ks by Borodin-Gorin-Wheeler\, Dauvergne and Galashin\, and a new family of
distributional identities relating the behavior of the oriented swap proc
ess in a surprising way to last passage percolation. Some of these identit
ies are still conjectural and hint at the existence of symmetries in the o
riented swap process\, multi-type TASEP and related processes that are sti
ll not understood. As a side treat for algebraic combinatorics enthusiasts
\, the RSK\, Burge and Edelman-Greene maps will also make an appearance.\n
LOCATION:https://researchseminars.org/talk/BIRS_20w5203/5/
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