Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{GraZei04}
\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
\mathnet{http://mi.mathnet.ru/tvp242}
\crossref{https://doi.org/10.4213/tvp242}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141336}
\zmath{https://zbmath.org/?q=an:1094.60066}
\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 148--155
\crossref{https://doi.org/10.1137/S0040585X97980920}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000228185300011}
Linking options:
  • https://www.mathnet.ru/eng/tvp242
  • https://doi.org/10.4213/tvp242
  • 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
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
    Statistics & downloads:
    Abstract page:337
    Full-text PDF :147
    References:55
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024