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UID:www.tcs.tifr.res.in/event/812
DTSTAMP:20230914T125939Z
SUMMARY:Compactness and Large Deviations
DESCRIPTION:Speaker: Chiranjib Mukherjee (Courant Institute of Mathematical
Sciences\nNew York University\nWarren Weaver Hall 1310\n251 Mercer Street
\nNew York\, NY 10012\nUnited States of America)\n\nAbstract: \nIn a reaso
nable topological space\, large deviation estimates essentially deal with
probabilities of events that are asymptotically (exponentially) small\, an
d in a certain sense\, quantify the rate of these decaying probabilities.
In such estimates\, upper bounds for such small probabilities often requir
e compactness of the ambient space\, which is often absent in problems ari
sing in statistical mechanics (for example\, distributions of local times
of Brownian motion in the full space $\\mathbb{R}^d$). Motivated by such a
problem\, we present a robust theory of ``translation-invariant compactic
ation" of probability measures in $\\mathbb{R}^d$. Thanks to an inherent s
hift-invariance of the underlying problem\, we are able to apply this abst
ract theory painlessly and solve a long standing problem in statistical me
chanics\, the mean-eld polaron problem.\n\nThis talk is based on joint wor
ks with S.R.S. Varadhan (New York)\, as well as with Erwin Bolthausen (Zur
ich) and Wolfgang Koenig (Berlin).\n
URL:https://www.tcs.tifr.res.in/web/events/812
DTSTART;TZID=Asia/Kolkata:20171003T160000
DTEND;TZID=Asia/Kolkata:20171003T170000
LOCATION:A-201 (STCS Seminar Room)
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