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BEGIN:VEVENT
SUMMARY:Reinforced Random Walks and Spin Systems
DTSTART:20230222T103000
DTEND:20230222T113000
DTSTAMP:20260502T223238Z
UID:5c936fc9beeb063e0e7c4a5806dedf0b8a3b573e5c81f7bbb0a5b931
CATEGORIES:Conferences - Seminars
DESCRIPTION:Andrew Swan - NYU-ECNU\, Shanghai\nTalk - Mathematics\nConnect
 ing random walks and spin systems are a collection of mysterious bridges k
 nown as isomorphism theorems. In the classical case\, these isomorphism th
 eorems relate the local times of simple random walks to the squares of Gau
 ssian free fields. In this talk\, I will discuss\nextensions of these clas
 sical isomorphism theorems to spin systems that take values in hyperbolic 
 and spherical geometries. Here\, the corresponding random walks are no lon
 ger Markovian\, but are now reinforced according to their history: in the 
 hyperbolic case\, the reinforcement is positive\, giving the vertex reinfo
 rced jump process (VRJP)\, whereas in the spherical case\, the reinforceme
 nt is negative\, giving the vertex diminished jump process\n(VDJP). In all
  three geometries -- flat\, hyperbolic\, and spherical -- the correspondin
 g isomorphism theorems exist due to symmetries of the underlying spin syst
 ems\, and when these symmetries are realised in more complicated spin syst
 ems\, the result is a 'field reinforced random walk'. Roughly speaking\, f
 ield reinforced random walks have jump rates that are mediated by a 'hidde
 n' spin system\, which itself is coupled to the local time field\,\nand I 
 will also discuss isomorphism theorems in this case.
LOCATION:MA B1 524 https://plan.epfl.ch/?room==MA%20B1%20524 https://epfl.
 zoom.us/j/68059355787
STATUS:CONFIRMED
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