Geodesic
On the lower bound of the spectrum of some mean-field models
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 164-171

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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. 
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     author = {B. L. Granovskii and A. I. Zeifman},
     title = {On the lower bound of the spectrum of some mean-field models},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a9/}
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B. L. Granovskii; A. I. Zeifman. On the lower bound of the spectrum of some mean-field models. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 164-171. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a9/