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SUMMARY:Ron Peled (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200915T153000Z
DTEND;VALUE=DATE-TIME:20200915T161000Z
DTSTAMP;VALUE=DATE-TIME:20201101T020414Z
UID:BIRS_20w5203/1
DESCRIPTION:Title: Euclidean random permutations\nby Ron Peled (Tel Aviv U
niversity) as part of BIRS workshop: Permutations and Probability\n\nAbstr
act: TBA\n
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BEGIN:VEVENT
SUMMARY:Evita Nestoridi (Princeton University)
DTSTART;VALUE=DATE-TIME:20200915T161500Z
DTEND;VALUE=DATE-TIME:20200915T165500Z
DTSTAMP;VALUE=DATE-TIME:20201101T020414Z
UID:BIRS_20w5203/2
DESCRIPTION:Title: Mixing results for the interchange and exclusion proces
ses with open boundaries\nby Evita Nestoridi (Princeton University) as par
t of BIRS workshop: Permutations and Probability\n\n\nAbstract\nAssign dis
trict cards to the vertices of a finite\, connected graph G(V\, E) with |V
|=n. The interchange process is a card shuffling scheme generated by flipp
ing the cards at the ends of the edges of the graph. The exclusion process
follows the same dynamics where instead each vertex is assigned one of tw
o colors. In this talk\, I will discuss recent developments concerning the
mixing time of these two processes on the interval of length n. I will fo
cus in particular on the asymmetric exclusion process with open boundaries
\, where particles are allowed to jump in and out from the ends of the int
erval. This is joint work with Gantert and Schmid.\n
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BEGIN:VEVENT
SUMMARY:Duncan Dauvergne (Princeton University)
DTSTART;VALUE=DATE-TIME:20200917T153000Z
DTEND;VALUE=DATE-TIME:20200917T161000Z
DTSTAMP;VALUE=DATE-TIME:20201101T020414Z
UID:BIRS_20w5203/3
DESCRIPTION:Title: The scaling limit of the longest increasing subsequence
\nby Duncan Dauvergne (Princeton University) as part of BIRS workshop: Per
mutations and Probability\n\n\nAbstract\nI will describe a framework for p
roving convergence to the directed landscape\, the central limit object in
the KPZ universality class. The directed landscape is a random scale-inva
riant `directed' metric on the plane. One highlight of this work is that t
he scaling limit of the longest increasing subsequence in a uniformly rand
om permutation is a geodesic in the directed landscape. Joint work with Ba
lint Virag.\n
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SUMMARY:Mickaël Maazoun (Oxford University)
DTSTART;VALUE=DATE-TIME:20200917T161500Z
DTEND;VALUE=DATE-TIME:20200917T165500Z
DTSTAMP;VALUE=DATE-TIME:20201101T020414Z
UID:BIRS_20w5203/4
DESCRIPTION:Title: Scaling limits of Baxter permutations and bipolar orien
tations\nby Mickaël Maazoun (Oxford University) as part of BIRS workshop:
Permutations 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 o
f uniform elements in various classes of pattern-avoiding permutations hav
e attracted a fair amount of attention lately. We show such a result for B
axter permutations\, a famous class of permutations avoiding generalized p
atterns.\n\nA remarkable bijection of Bousquet-Mélou\, Bonichon and Fusy
(2010) with bipolar orientations\, a type of decorated planar maps\, allow
s us to express a Baxter permutation in terms of the relationship between
the mating-of-trees encoding (Kenyon\, Miller\, Sheffield\, Wilson\, 2015)
of a bipolar orientation and the one of its dual map. This was already st
udied by Gwynne\, Holden\, Sun (2016)\, and our main result can be seen as
an improvement of theirs.\n\nThe main step of our approach is to encode t
he problem in a "coalescent-walk" process\, which converges to the coalesc
ing process obtained when solving the perturbed Tanaka SDE (Prokaj\, 2011)
with the same Brownian noise at different starting times. If time allows\
, I will talk about the robustness of the method and possible generalizati
ons.\n
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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:20201101T020414Z
UID:BIRS_20w5203/5
DESCRIPTION:Title: Distributional identities and absorbing time asymptotic
s in the oriented swap process\nby Dan Romik (University of California Dav
is) as part of BIRS workshop: Permutations and Probability\n\n\nAbstract\n
The oriented swap process is a model for a random sorting network\, in whi
ch N particles labeled 1\,...\,N arranged on the discrete lattice [1\,N] s
tart out in increasing order and then perform successive adjacent swaps at
random times until they reach the reverse configuration N\,...\,1. An ope
n problem from 2009 asked for the limiting law of the absorbing time of th
e process. In recent joint works with Bisi-Cunden-Gibbons and Bufetov-Gori
n\, we resolved 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 an
d how it came to be discovered and proved\, which involves connections to
recent works by Borodin-Gorin-Wheeler\, Dauvergne and Galashin\, and a new
family of distributional identities relating the behavior of the oriented
swap process in a surprising way to last passage percolation. Some of the
se identities are still conjectural and hint at the existence of symmetrie
s in the oriented swap process\, multi-type TASEP and related processes th
at are still not understood. As a side treat for algebraic combinatorics e
nthusiasts\, the RSK\, Burge and Edelman-Greene maps will also make an app
earance.\n
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