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SUMMARY:Hypocoercivity without changing the scalar product
DTSTART:20261202T150000
DTEND:20261202T160000
DTSTAMP:20261109T192646Z
UID:565ccab07f264047cfd3b71e97440702eea40ae07ed388f1a9813cd5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professor Gabriel Stoltz\, CERMICS\, Ecole des Ponts & MATHERI
 ALS\, Inria Paris\nHypocoercive methods allow to prove the longtime conver
 gence of the law of degenerate stochastic processes such as Langevin dynam
 ics or random time HMC. From a technical viewpoint\, these approaches usua
 lly involve a change of scalar product (as in the H^1 approach à la Villa
 ni\, or the L^2 approach of Hérau and Dolbeault/Mouhot/Schmeiser). I will
  discuss two approaches which do not require such a change of scalar produ
 ct\, and henceforth provide the current sharpest quantitative estimates on
  the resolvent of the generator\, which makes it possible for instance to 
 bound the variance of estimators based on time averages along a realizatio
 n of the process. The first approach\, originally due to Armstrong/Mourrat
 \, was adapted to dynamics on the whole space by Cao/Lu/Wang\, and is base
 d on space-time Poincare inequalities. I will review some progress made wi
 th Giovanni Brigati on better understanding the algebraic structures behin
 d this method\, and possibly mention extensions to weak/weighted Poincaré
  inequalities (in collaboration with Lihan Wang and Andi Wang). The second
  approach\, developed with Etienne Bernard\, Max Fathi and Antoine Levitt\
 , is based on Schur complements and provides direct bounds on the resolven
 t using the specific saddle-point like structure of the generator under an
  appropriate orthogonal decomposition of L^2.\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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