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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 1, Pages 164–171
DOI: https://doi.org/10.4213/tvp242 (Mi tvp242) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

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

B. L. Granovskiia, A. I. Zeifmanb

a Technion – Israel Institute of Technology
b Vologda State Pedagogical University
Full-text PDF (940 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp242
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
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 1, Pages 148–155
DOI: https://doi.org/10.1137/S0040585X97980920
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. L. Granovskii, A. I. Zeifman, “On the lower bound of the spectrum of some mean-field models”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 164–171; Theory Probab. Appl., 49:1 (2005), 148–155
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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\pages 148--155
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  • https://www.mathnet.ru/eng/tvp/v49/i1/p164
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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