In 1999 Catoni determined the critical rate $H_3$ for the relaxation time of generalized Metropolis algorithms, models for which the speed of convergence to equilibrium can be strongly influenced by the effects of a possible almost periodicity. We recover this result with the help of Dobrushin's coefficient and give characterizations of $H_3$ in terms of other ergodic constants. In particular, we prove that it also governs the large deviation behavior of the singular gap for a sufficiently large but finite number of iterations of the underlying kernel at low temperature.
Publié le : 2002-11-14
Classification:
Generalized Metropolis algorithm at low temperature,
critical rate for relaxation times,
Dobrushin's coefficient and coupling,
spectral gaps and singular values,
classical or modified logarithmic Sobolev inequalities,
delaying effect for ergodic constants,
simulated annealing,
60J10,
65C40,
49K45,
37A25,
15A18
@article{1037125871,
author = {Miclo, L.},
title = {About relaxation time of finite generalized Metropolis algorithms},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 1492-1515},
language = {en},
url = {http://dml.mathdoc.fr/item/1037125871}
}
Miclo, L. About relaxation time of finite generalized Metropolis algorithms. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 1492-1515. http://gdmltest.u-ga.fr/item/1037125871/