B. L. Granovskii, A. I. Zeifman, “On the lower bound of the spectrum of some mean-field models”, Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1,Pages <nobr>164

This article is cited in 10 papers

Short Communications

On the lower bound of the spectrum of some mean-field models

B. L. Granovskii^a, A. I. Zeifman^b

^a Technion – Israel Institute of Technology
^b Vologda State Pedagogical University

Abstract: We find the lower bound of the spectrum of the $q$-matrix for a variety of mean-field models, as the number of interacting sites goes to infinity. We also make a comparative study of the asymptotic behavior of the lower bound and the spectral gap and establish a characterization of a class of mean-field models for which both bounds of the spectrum attain their extremal values. The results are obtained with the help of the method suggested by the second author in the late 1980s.

Keywords: mean-field models, birth-death processes, random walks on graphs, spectrum of the generator, maximal and minimal rates of exponential convergence, spectral gap.

Received: 19.12.2001
Revised: 30.06.2003

DOI: 10.4213/tvp242