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BEGIN:VEVENT
UID:4b6006f93ab95ae6be4b04e1ad576262
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20250204T122836
SUMMARY: Random-cluster model on $\mathbb{Z}^2$ at the transition point
LOCATION:705
DESCRIPTION:<p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: relative
 ; color: #212121; font-size: 11pt; font-style: normal; font-weight: 400; fo
 nt-family: Lato, sans-serif; line-height: 1.6667; letter-spacing: normal; o
 rphans: 2; text-align: start; text-indent: 0px; text-transform: none; widow
 s: 2; word-spacing: 0px; white-space: normal;"><span style="font-family: La
 to, Arial; font-variant: normal; font-weight: bold;">Speaker</span><span st
 yle="font-variant: normal;">:&nbsp;</span><a href="https://www.uibk.ac.at/m
 athematik/personal/aglazman/" target="_blank" rel="noopener" style="color: 
 inherit; text-decoration: none;"><span style="color: #006580; font-variant:
  normal; text-decoration: underline;">Alexander Glazman</span></a><span sty
 le="font-variant: normal;">&nbsp;(University of Innsbruck)</span></p><p dir
 ="ltr" style="margin: 12px 0px 0px; outline: none; position: relative; colo
 r: #212121; font-size: 11pt; font-style: normal; font-weight: 400; font-fam
 ily: Lato, sans-serif; line-height: 1.6667; letter-spacing: normal; orphans
 : 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; 
 word-spacing: 0px; white-space: normal;"><span style="font-family: Lato, Ar
 ial; font-variant: normal; font-weight: bold;">Title</span><span style="fon
 t-variant: normal;">: Random-cluster model on $mathbb{Z}^2$ at the transiti
 on point</span></p><p dir="ltr" style="margin: 12px 0px 0px; outline: none;
  position: relative; color: #212121; font-size: 11pt; font-style: normal; f
 ont-weight: 400; font-family: Lato, sans-serif; line-height: 1.6667; letter
 -spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-tra
 nsform: none; widows: 2; word-spacing: 0px; white-space: normal;"><span sty
 le="font-family: Lato, Arial; font-variant: normal; font-weight: bold;">Abs
 tract</span><span style="font-variant: normal;">: The random-cluster model 
 is defined on subgraphs of $mathbb{Z}^2$ and has two parameters: cluster-we
 ight $q&gt;0$ and edge-probability $0&lt;p&lt;1$. It is classical that, for
  each $qgeq 1$, the model undergoes a percolation phase transition when $p=
 p_c(q)$. Beffara and Duminil-Copin in 2010 computed $p_c(q)$, and later wor
 ks established the type of the phase transition: it is continuous when $1 l
 eq q leq 4$ and discontinuous when $q&gt;4$. The former is characterised by
  Russo-Seymour-Welsh estimates, while the latter asserts non-uniqueness of 
 the infinite-volume DLR/Gibbs measure.</span></p><p dir="ltr" style="margin
 : 12px 0px 0px; outline: none; position: relative; color: #212121; font-siz
 e: 11pt; font-style: normal; font-weight: 400; font-family: Lato, sans-seri
 f; line-height: 1.6667; letter-spacing: normal; orphans: 2; text-align: sta
 rt; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; w
 hite-space: normal;"><span style="font-variant: normal;">In this talk we re
 visit both parts of this diagram. When $1 leq q leq 4$, we give a new proof
  of continuity that does not use parafermionic observable, nor Bethe Ansatz
 . When $q&gt;4$, we establish invariance principle under Dobrushin boundary
  conditions: the interface converges to the Brownian bridge. Both arguments
  rely on the Baxter-Kelland-Wu correspondence that relates the random-clust
 er model to a certain height function (six-vertex model). Remarkably, we ob
 tain also some result when $q&lt;1$, though only at the self-dual point.</s
 pan></p><p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: 
 relative; color: #212121; font-size: 11pt; font-style: normal; font-weight:
  400; font-family: Lato, sans-serif; line-height: 1.6667; padding-bottom: 0
 px; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px
 ; text-transform: none; widows: 2; word-spacing: 0px; white-space: normal;"
 ><span style="font-variant: normal;">Joint works with Moritz Dober, Piet La
 mmers and Sebastien Ott.</span></p>
CONTACT:Alexander Glazman
DTSTAMP:20260828T122213
DTSTART;TZID=America/New_York:20250205T104500
DTEND;TZID=America/New_York:20250205T234500
SEQUENCE:0
TRANSP:OPAQUE
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