About Relaxation Time of Finite Generalized Metropolis Algorithms

• Published in: The Annals of applied probability Vol. 12; no. 4; pp. 1492 - 1515
• Main Author: Miclo, L.
• Format: Journal Article
• Language: English
• Published: Institute of Mathematical Statistics 01-11-2002; The Institute of Mathematical Statistics
• Subjects: 15A18; 37A25; 49K45; 60J10; 65C40; classical or modified logarithmic Sobolev inequalities; Constant coefficients; critical rate for relaxation times; delaying effect for ergodic constants; Dobrushin's coefficient and coupling; Ergodic theory; Generalized Metropolis algorithm at low temperature; Infrared radiation; Low temperature; Markov chains; Mathematical minima; Mathematics; Metropolitan areas; Respect; Simulated annealing; spectral gaps and singular values
• ISSN: 1050-5164; 2168-8737
• DOI: 10.1214/aoap/1037125871

In 1999 Catoni determined the critical rate H3 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 H3 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.