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VERSION:2.0
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CALSCALE:GREGORIAN
X-WR-CALNAME:MIT Probability Seminar
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20261008T102540Z
UID:tag:localist.com\,2008:EventInstance_41421358123551
DTSTART:20221107T211500Z
DTEND:20221107T221500Z
DESCRIPTION:Speaker: Dor Elboim (Princeton University) \n\nTitle: Infinite 
 cycles in the interchange process in five dimensions.\n\nAbstract: \n\nIn 
 the interchange process on a graph G=(V\,E)\, there is a particle on each 
 vertex of the graph and an independent Poisson clock on each one of the ed
 ges. Once the clock of an edge rings\, the two particles on the two sides 
 of the edge switch. After time t\, the particles are permuted according to
  a random permutation $\\pi_t:V\\to V$. A famous conjecture of Balint Toth
  states that the following holds when $G=\\mathbb$ $Z^d$ :\n \n\n(1) If d=
 2\, then the permutation $\\pi_t$ contains only finite cycles for all t>0.
 \n(2) If $d\\ge 3$\, then there exists $t_c$ such that for $tt_c$\, $\\pi_
 t$ contains infinite cycles.\n\nWe prove the existence of infinite cycles 
 for all $d\\ge 5$ and all $t$ sufficiently large. To this end\, we study t
 he cyclic time random walk obtained by exposing the cycle of the origin in
  $\\pi_t$. We show that this walk is diffusive using a multiscale inductiv
 e argument.\n\nThis is a joint work with Allan Sly.
GEO:42.358262;-71.090045
LOCATION:Building 2\, 2-147
SUMMARY:MIT Probability Seminar
URL;VALUE=URI:https://calendar.mit.edu/event/mit_probability_seminar_202211
 07
CATEGORIES:Conferences/Seminars/Lectures
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