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November 2002 About relaxation time of finite generalized Metropolis algorithms
L. Miclo
Ann. Appl. Probab. 12(4): 1492-1515 (November 2002). DOI: 10.1214/aoap/1037125871


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.


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L. Miclo. "About relaxation time of finite generalized Metropolis algorithms." Ann. Appl. Probab. 12 (4) 1492 - 1515, November 2002.


Published: November 2002
First available in Project Euclid: 12 November 2002

zbMATH: 1012.60065
MathSciNet: MR1936601
Digital Object Identifier: 10.1214/aoap/1037125871

Primary: 60J10
Secondary: 15A18‎ , 37A25 , 49K45 , 65C40

Keywords: classical or modified logarithmic Sobolev inequalities , critical rate for relaxation times , delaying effect for ergodic constants , Dobrushin's coefficient and coupling , Generalized Metropolis algorithm at low temperature , simulated annealing , spectral gaps and singular values

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 4 • November 2002
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