BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Cutoff phenomenon for Dyson Ornstein Uhlenbeck process
DTSTART;VALUE=DATE-TIME:20240306T160000
DTEND;VALUE=DATE-TIME:20240306T173000
DTSTAMP;VALUE=DATE-TIME:20240422T013533Z
UID:b895583c4a3cc36267d21fabda41bc6253ab6c480729b038d104e27c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Djalil Chafaï (Paris)\nWe study the Dyson-Ornstein-Uhlenbeck
diffusion process\, an evolving gas of interacting particles. Its invarian
t law is the beta Hermite ensemble of random matrix theory\, a non-product
log-concave distribution. We explore the convergence to equilibrium of th
is process for various distances or divergences\, including total variatio
n\, relative entropy\, and transportation cost. When the number of particl
es is sent to infinity\, we show that a cutoff phenomenon occurs: the dist
ance to equilibrium vanishes abruptly at a critical time. A remarkable fea
ture is that this critical time is independent of the parameter beta that
controls the strength of the interaction\, in particular the result is ide
ntical in the non-interacting case\, which is nothing but the Ornstein-Uhl
enbeck process. We also provide a complete analysis of the non-interacting
case that reveals some new phenomena. Our work relies among other ingredi
ents on convexity and functional inequalities\, exact solvability\, exact
Gaussian formulas\, coupling arguments\, stochastic calculus\, variational
formulas and contraction properties. This work leads\, beyond the specifi
c process that we study\, to questions on the high-dimensional analysis of
heat kernels of curved diffusions. This is a joint work with Jeanne Bours
ier and Cyril Labbé.
LOCATION:Bernoulli center https://maps.app.goo.gl/LGa7ei1hQkCkkHN1A
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR