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SUMMARY:Invariant measures of the infinite Atlas model: domains of attract
 ion\, extremality\, and equilibrium fluctuations - Amarjit Budhiraja (Univ
 ersity of North Carolina)
DTSTART:20240723T140000Z
DTEND:20240723T150000Z
UID:TALK218695@talks.cam.ac.uk
DESCRIPTION:The infinite Atlas model describes a countable system of compe
 ting Brownian particles where the lowest particle gets a unit upward drift
  and the rest evolve as standard Brownian motions. The stochastic process 
 of gaps between the particles in the infinite Atlas model has a one parame
 ter family {p(a)\, a > 0} of product form mutually singular stationary dis
 tributions. We say that an initial distribution of gaps is in the weak dom
 ain of attraction of the stationary measure p(a) if the time averaged laws
  of the stochastic process of the gaps\, when initialized using that distr
 ibution\, converge to p(a) weakly in the large time limit. We provide gene
 ral sufficient conditions on the initial gap distribution of the Atlas par
 ticles for it to lie in the weak domain of attraction of p(a) for each a. 
 Results on extremality and ergodicity of p(a) will be presented. Finally\,
  time permitting\, we will describe some recent results on fluctuations of
  the Atlas model from inhomogeneous stationary profiles.&nbsp\;\nThis is b
 ased on joint work with Sayan Banerjee and Peter Rudzis.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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