메뉴 건너뛰기




Volumn 114, Issue 4, 1999, Pages 431-485

Relations entre isopérimétrie et trou spectral pour les chaînes de Markov finies

Author keywords

Finite Markov kernels; Isoperimetry, (modified) spectral gaps; Paths and Poincar 's methods; Reversible probabilities; Underlying graphs and trees

Indexed keywords


EID: 0033173868     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050231     Document Type: Article
Times cited : (17)

References (17)
  • 2
    • 20344362744 scopus 로고
    • A lower bound for the smallest eigenvalue of the Laplacien
    • Gunning, R.C. (ed). Princeton University Press
    • Cheeger, J. : A lower bound for the smallest eigenvalue of the Laplacien. In : Gunning, R.C. (ed), Problems in Analysis : A Symposium in Honor of S. Bochner, pages 195-199. Princeton University Press (1970)
    • (1970) Problems in Analysis : A Symposium in Honor of S. Bochner , pp. 195-199
    • Cheeger, J.1
  • 3
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for finite Markov chains
    • Diaconis, P., Saloff-Coste, L. : Logarithmic Sobolev inequalities for finite Markov chains. The Ann. App. Probab. 6(3), 695-750 (1996)
    • (1996) The Ann. App. Probab. , vol.6 , Issue.3 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 4
    • 0002740591 scopus 로고
    • Geometric bounds for eigenvalues of Markov chains
    • Diaconis, P., Stroock, D. : Geometric bounds for eigenvalues of Markov chains. The Ann. App. Probab. 1(1), 36-61 (1991)
    • (1991) The Ann. App. Probab. , vol.1 , Issue.1 , pp. 36-61
    • Diaconis, P.1    Stroock, D.2
  • 8
    • 0000941412 scopus 로고
    • 2 spectrum for Markov chains and Markov processes : A generalization of Cheeger's inequality
    • 2 spectrum for Markov chains and Markov processes : a generalization of Cheeger's inequality. Transactions of the American mathematical society. 309(2), 557-580 (1988)
    • (1988) Transactions of the American Mathematical Society , vol.309 , Issue.2 , pp. 557-580
    • Lawler, G.1    Sokal, A.2
  • 9
    • 0001525416 scopus 로고
    • A simple analytic proof of an inequality by P. Buser
    • Ledoux, M. : A simple analytic proof of an inequality by P. Buser. Proceedings of the American mathematical society. 121(3), 951-959 (1994)
    • (1994) Proceedings of the American Mathematical Society , vol.121 , Issue.3 , pp. 951-959
    • Ledoux, M.1
  • 10
    • 85033963876 scopus 로고    scopus 로고
    • Trous spectraux à basse température : Un contre-exemple à un comportement asymptotique escompté
    • Miclo, L. : Trous spectraux à basse température : un contre-exemple à un comportement asymptotique escompté. A paraître dans le Séminaire de Probabilités XXXII, (1997)
    • (1997) A Paraître dans le Séminaire de Probabilités XXXII
    • Miclo, L.1
  • 11
    • 84996139082 scopus 로고    scopus 로고
    • Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies
    • Miclo, L. : Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies. ESAIM : P&S 2, 1-21 (1998)
    • (1998) ESAIM : P&S , vol.2 , pp. 1-21
    • Miclo, L.1
  • 13
    • 0000665059 scopus 로고
    • Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
    • Rothaus, O.S. : Analytic Inequalities, Isoperimetric Inequalities and Logarithmic Sobolev Inequalities. J. Funct. Anal. 64, 296-313 (1985)
    • (1985) J. Funct. Anal. , vol.64 , pp. 296-313
    • Rothaus, O.S.1
  • 15
    • 0001671336 scopus 로고
    • Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator
    • Sawyer, E. : Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator. Transactions of the American Mathematical Society. 281(1), 329-337 (1984)
    • (1984) Transactions of the American Mathematical Society , vol.281 , Issue.1 , pp. 329-337
    • Sawyer, E.1
  • 16
    • 0003570325 scopus 로고
    • Non-negative Matrices and Markov chains
    • Springer-Verlag
    • Seneta, E. : Non-negative Matrices and Markov Chains. Springer Series in Statistics. Springer-Verlag (1981)
    • (1981) Springer Series in Statistics
    • Seneta, E.1
  • 17
    • 84971804758 scopus 로고
    • Improved bounds for mixing rates of Markov chains and multicommodity flow
    • Sinclair, A. : Improved bounds for mixing rates of Markov chains and multicommodity flow. Combinatorics, Probability and Computing, 1, 351-370 (1992)
    • (1992) Combinatorics, Probability and Computing , vol.1 , pp. 351-370
    • Sinclair, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.