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SUMMARY:Optimal non-symmetric Fokker-Planck equation for the convergence t
 o a given equilibrium - Anton Arnold (Technische Universität Wien)
DTSTART:20220110T133000Z
DTEND:20220110T143000Z
UID:TALK166645@talks.cam.ac.uk
DESCRIPTION:We are concerned with finding Fokker-Planck equations in whole
  space with the fastest exponential decay towards a given equilibrium. For
  a prescribed\, anisotropic Gaussian we determine a non-symmetric Fokker-P
 lanck equation with linear drift that shows the highest exponential decay 
 rate for the convergence of its solutions towards equilibrium. At the same
  time it has to allow for a decay estimate with a multiplicative constant 
 arbitrarily close to its infimum. This infimum is 1\, corresponding to the
  high-rotational limit in the Fokker-Planck drift.\nSuch an &ldquo\;optima
 l&rdquo\; Fokker-Planck equation is constructed explicitly with a diffusio
 n matrix of rank one\, hence being hypocoercive. The proof is based on the
  recent result that the $L^2$-propagator norms of the Fokker-Planck equati
 on and of its drift-ODE coincide.\nFinally we give an outlook onto using F
 okker-Planck equations with t-dependent coefficients.\nReferences:\n* A. A
 rnold\, B. Signorello: Optimal non-symmetric Fokker-Planck equation for th
 e convergence to a given equilibrium\, preprint 2021.\n* A. Arnold\, C. Sc
 hmeiser\, B. Signorello. Sharp decay estimates and $L^2$-propagator norm f
 or Fokker-Planck equations with linear drift\, preprint 2020.
LOCATION:Seminar Room 1\, Newton Institute
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