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SUMMARY:Quasi-stationarity and metastability: Insights from weakly interac
 ting particle systems and applications to SPDE
DTSTART:20240205T150000
DTEND:20240205T155000
DTSTAMP:20260916T225821Z
UID:b5d1b2073473d93e382574fdb64576386d17f65cfadf6a76c37ad501
CATEGORIES:Conferences - Seminars
DESCRIPTION:Zachary Adams (Max Planck Institute)\nAbstract. Many models fr
 om physics and the life sciences exhibit metastable behaviour -- that is\,
  behaviour that appears to be stable over some time scale\, but dies out o
 r significantly changes on longer time scales. For instance\, consider a 
 system of N particles moving as Brownian motions interacting via an attrac
 tive potential (such as the Glauber dynamics associated with the classical
  mean-field O(2) spin system of statistical mechanics). \nIn the large pa
 rticle limit of such systems\, the empirical measure of such systems is kn
 own to converge to a nonlocal parabolic PDE of McKean-Vlasov type.  While
  the McKean-Vlasov system is known to possess no non-trivial stationary so
 lutions\, numerical experiments demonstrate the existence of an almost-syn
 chronized state that persists over a long time scale. \nIn this talk\, we
  characterize this almost-synchronized state and the time scale on which i
 t persists using methods involving sub-Markov semigroups\, quasi-stationar
 y distributions\, and the spectral theory of Schrödinger operators applie
 d to the finite particle system. Control on the time scale in terms of th
 e noise amplitude and particle number are obtained in total variation and 
 Wasserstein distance. Time permitting\, we will discuss how the insights 
 gained from the study of metastability in many particle systems may lead t
 o the application of similar methods to metastable behaviour in SPDE.
LOCATION:MA B1 504
STATUS:CONFIRMED
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