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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 164–171 (Mi tvp242)  

This article is cited in 7 scientific papers (total in 7 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

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.

DOI: https://doi.org/10.4213/tvp242

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English version:
Theory of Probability and its Applications, 2005, 49:1, 148–155

Bibliographic databases:

Received: 19.12.2001
Revised: 30.06.2003

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
\by B.~L.~Granovskii, A.~I.~Zeifman
\paper On the lower bound of the spectrum of some mean-field models
\jour Teor. Veroyatnost. i Primenen.
\yr 2004
\vol 49
\issue 1
\pages 164--171
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 148--155

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  • https://doi.org/10.4213/tvp242
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zeifman A., Chegodaev A., Shilova G., “Almost absorbing continuous-time Markov's chains on finite state space”, International Conference on Modelling of Business, Industrial and Transport Systems, 2008, 213–217  isi
    2. E. van Doorn, A. I. Zeifman, T. L. Panfilova, “Bounds and Asymptotics for the Rate of Convergence of Birth-Death Processes”, Theory Probab. Appl., 54:1 (2010), 97–113  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. van Doorn E.A., van Foreest N.D., Zeifman A.I., “Representations for the extreme zeros of orthogonal polynomials”, J. Comput. Appl. Math., 233:3 (2009), 847–851  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Ya. A. Satin, A. I. Zeifman, A. V. Korotysheva, S. Ya. Shorgin, “Ob odnom klasse markovskikh sistem obsluzhivaniya”, Inform. i ee primen., 5:4 (2011), 18–24  mathnet
    5. Zeifman A.I. Korolev V.Yu., “Two-Sided Bounds on the Rate of Convergence For Continuous-Time Finite Inhomogeneous Markov Chains”, Stat. Probab. Lett., 103 (2015), 30–36  crossref  mathscinet  zmath  isi  elib  scopus
    6. Zeifman A.I., Korolev V.Yu., Satin Ya.A., Kiseleva K.M., “Lower Bounds For the Rate of Convergence For Continuous-Time Inhomogeneous Markov Chains With a Finite State Space”, Stat. Probab. Lett., 137 (2018), 84–90  crossref  mathscinet  zmath  isi  scopus
    7. Zeifman I A., Satin Y.A., Kiseleva K.M., “On Obtaining Sharp Bounds of the Rate of Convergence For a Class of Continuous-Time Markov Chains”, Stat. Probab. Lett., 161 (2020), 108730  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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