Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies
ESAIM: Probability and Statistics, Tome 2 (1998), pp. 1-21. 
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     author = {Miclo, Laurent},
     title = {Une variante de l'in\'egalit\'e de {Cheeger} pour les cha{\^\i}nes de {Markov} finies},
     journal = {ESAIM: Probability and Statistics},
     pages = {1--21},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1998},
     mrnumber = {1609632},
     zbl = {0929.60051},
     language = {fr},
     url = {http://archive.numdam.org/item/PS_1998__2__1_0/}
}
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Miclo, Laurent. Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies. ESAIM: Probability and Statistics, Tome 2 (1998), pp. 1-21. http://archive.numdam.org/item/PS_1998__2__1_0/

Ayoub, R. ( 1963). An introduction to the analytic theory of numbers. Mathematical Surveys 10, American Mathematical Society. | MR | Zbl

Cheeger, J. ( 1970). A lower bound for the smallest eigenvalue of the Laplacien. In Problems in Analysis: A Symposium in Honor of S. Bochner, R.C. Gunning editor, Princeton University Press, 195-199. | MR | Zbl

Deuschel, J.-D. and Mazza, C. ( 1994). L2 convergence of time nonhomogeneous Markov processes: I. spectral estimates. Ann. Appl. Prob. 4 1012-1056. | MR | Zbl

Diaconis, P. ( 1988). Group Representations in Probability and Statistics. Lecture Notes-Monograph Series 11, Institute of Mathematical Statistics. | MR | Zbl

Diaconis, P. and Stroock, D. ( 1991). Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Prob. 1 36-61. | MR | Zbl

Freidlin, M.I. and Wentzell, A.D. ( 1984). Random Perturbations of Dynamical Systems. A Series of Comprehensive Studies in Mathematics 260, Springer-Verlag. | MR | Zbl

Götze, F. ( 1991). Rate of convergence of simulated annealing processes. Préprint de l'Universität Bielefeld. | MR

Holley, R. and Stroock, D. ( 1988). Simulated annealing via Sobolev inequalities. Communications in Mathematical Physics 115 553-569. | MR | Zbl

Lawler, G. and Sokal A. ( 1988). Bounds on the L2 spectrum for Markov chains and Markov processes: a generalization of Cheeger's inequality. Transactions of the American Mathematical Society 309 557-580. | MR | Zbl

Mathieu, P. ( 1997). Hitting times and spectral gap inequalities. Annales de l'Institut Henri Poincaré 33 437-465. | EuDML | Numdam | MR | Zbl

Miclo, L. ( 1992). Recuit simulé sans potentiel sur un ensemble fini. In Séminaire de Probabilités XXVI, J. Azéma, P.A. Meyer and M. Yor editors, Lecture Notes in Mathematics 1526, Springer-Verlag, 47-60. | EuDML | Numdam | MR | Zbl

Miclo, L. ( 1997). Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies. In Séminaire de Probabilités XXXI, J. Azéma, M. Emery and M. Yor editors, Lecture Notes in Mathematics 1655, Springer-Verlag, Berlin, 136-167. | EuDML | Numdam | MR | Zbl

Mohar, B. ( 1989). Isoperimetric numbers of graphs. J. Comb. Theory B 47 274-291. | MR | Zbl

Pignataro, T. and Sullivan, D. ( 1986). Ground state and lowest eigenvalue of the Laplacian for non-compact hyperbolic surfaces. Communic. Math. Physics 104 529-535. | MR | Zbl

Saloff-Coste, L. ( 1997). Lectures on finite Markov chains. In Lectures on Probability Theory and Statistics. École d'Été de Probabilités de Saint-Flour XXVI-1996, P. Bernard editor, Lecture Notes in Mathematics 1665, Springer-Verlag, Berlin. | MR | Zbl

Trouvé, A. ( 1996). Cycle decompositions and simulated annealing. Society for Industrial and Applied Mathematics, Journal on Control and Optimization 34 966-986. | MR | Zbl

Trouvé, A. ( 1996). Rough large deviation estimates for the optimal convergence speed exponent of generalized simulated annealing algorithms. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 32 299-348. | EuDML | Numdam | MR | Zbl