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SUMMARY:A diffusion  limit for a model of interacting spins/queues  with  
  log-linear  interaction - Vadim Shcherbakov (Royal Holloway\, University 
 of London)
DTSTART:20240806T143000Z
DTEND:20240806T150000Z
UID:TALK218032@talks.cam.ac.uk
DESCRIPTION:This talk concerns a &nbsp\;diffusion limit &nbsp\;for &nbsp\;
 an interacting spin model defined in terms of a multi-component &nbsp\;Mar
 kov chain &nbsp\;whose components (spins) &nbsp\;are indexed by vertices o
 f a finite graph. The spins take values in a finite &nbsp\;set of non-nega
 tive integers and evolve subject to &nbsp\;a graph based log-linear &nbsp\
 ;interaction. &nbsp\;We show that if the set of possible spin values expan
 ds to the set of all non-negative integers\, then a time-scaled and normal
 ised version of the Markov chain converges to a system of interacting Orns
 tein-Uhlenbeck processes reflected at the origin. This limit &nbsp\;is aki
 n to heavy traffic limits in queueing (and our model can be naturally inte
 rpreted as a queueing model). &nbsp\; Our proof draws on developments &nbs
 p\;in queueing theory &nbsp\; &nbsp\; and relies on &nbsp\;martingale meth
 ods. Although the idea of the proof is similar to those used &nbsp\;for ob
 taining heavy traffic limits\, &nbsp\;some modifications are required due 
 to the presence of interaction. &nbsp\;The talk is based on the joint work
  with Anatolii Puhal'skii.
LOCATION:External
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