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SUMMARY:Invariant Measures of the Infinite Atlas Model: Domains of Attract
 ion\, Extremality\, and Equilibrium Fluctuations.
DTSTART:20230504T160000
DTEND:20230504T165000
DTSTAMP:20260916T225958Z
UID:e1e3dd73682123bff909d9cf8584034ad6d686470b54182b8af015ba
CATEGORIES:Conferences - Seminars
DESCRIPTION:Amarjit Budhiraja (Univ North Carolina)\n\nAbstract: The infin
 ite Atlas model describes a countable system of competing Brownian particl
 es where the lowest particle gets a unit upward drift and the rest evolve 
 as standard Brownian motions. The stochastic process of gaps between the p
 articles in the infinite Atlas model does not have a unique stationary dis
 tribution and in fact there is a one parameter family {p(a)\,a>= 0} of pr
 oduct form mutually singular stationary distributions. \nWe say that an i
 nitial distribution of gaps is in the weak domain of attraction of the sta
 tionary measure p(a) if the time averaged laws of the stochastic process 
 of the gaps\, when initialized using that distribution\, converge to p(a)
  weakly in the large time limit. We provide general sufficient conditions 
 on the initial gap distribution of the Atlas particles for it to lie in th
 e weak domain of attraction of p(a) for each a. Results on extremality an
 d ergodicity of p(a) will also be presented. Finally\, we will introduce 
 a SPDE that describes equilibrium fluctuations associated with p(a). This 
 is based on joint works with Sayan Banerjee and Peter Rudzis.\n 
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STATUS:CONFIRMED
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