BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Cutoff phenomenon for Dyson Ornstein Uhlenbeck process
DTSTART:20240306T160000
DTEND:20240306T173000
DTSTAMP:20260925T170646Z
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