Séminaire du LPTMS: Alexei Chepelianskii (LPS)

Monte Carlo sampling: convergence, localization transition and optimality

Alexei Chepelianskii  (Laboratoire de Physique des Solides)

Onsite + zoom (ID meeting: 935 9787 7477, Passcode: 154gyz).

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. From a combination of analytical and numerical approaches, we study their convergence properties towards the steady state. We show that the deviations from the target steady-state distribution features a localization transition as a function of the characteristic length of the attempted jumps defining the random walk in a Metropolis scheme. This transition changes drastically the error which is introduced by incomplete convergence. Remarkably, the localization transition occurs for parameters that also provide the optimal Monte Carlo convergence speed. We show that the relaxation of the error in the localized regime has some similarities with relaxation in a greedy Monte Carlo algorithm where jumps always  occur to lower energy sites (zero temperature limit). In both cases relaxation is described by a self-similar ansatz instead of being dominated by the  eigenmode with the slowest relaxation rate as in diffusion problems.

 


Date/Time : 12/10/2021 - 11:00 - 12:30

Location : Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530

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