Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies

Laurent Miclo

ESAIM: Probability and Statistics (1998)

  • Volume: 2, page 1-21
  • ISSN: 1292-8100

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Miclo, Laurent. "Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies." ESAIM: Probability and Statistics 2 (1998): 1-21. <http://eudml.org/doc/104249>.

@article{Miclo1998,
author = {Miclo, Laurent},
journal = {ESAIM: Probability and Statistics},
keywords = {finite reversible Markov kernels; isoperimetric constant; modified spectral gap; optimal linear variants of the Cheeger's inequality; generalized simulated annealing algorithms},
language = {fre},
pages = {1-21},
publisher = {EDP Sciences},
title = {Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies},
url = {http://eudml.org/doc/104249},
volume = {2},
year = {1998},
}

TY - JOUR
AU - Miclo, Laurent
TI - Une variante de l'inégalité de Cheeger pour les chaînes de Markov finies
JO - ESAIM: Probability and Statistics
PY - 1998
PB - EDP Sciences
VL - 2
SP - 1
EP - 21
LA - fre
KW - finite reversible Markov kernels; isoperimetric constant; modified spectral gap; optimal linear variants of the Cheeger's inequality; generalized simulated annealing algorithms
UR - http://eudml.org/doc/104249
ER -

References

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  2. 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. Zbl0212.44903MR402831
  3. Deuschel, J.-D. and Mazza, C. ( 1994). L2 convergence of time nonhomogeneous Markov processes: I. spectral estimates. Ann. Appl. Prob. 4 1012-1056. Zbl0819.60063MR1304771
  4. Diaconis, P. ( 1988). Group Representations in Probability and Statistics. Lecture Notes-Monograph Series 11, Institute of Mathematical Statistics. Zbl0695.60012MR964069
  5. Diaconis, P. and Stroock, D. ( 1991). Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Prob. 1 36-61. Zbl0731.60061MR1097463
  6. Freidlin, M.I. and Wentzell, A.D. ( 1984). Random Perturbations of Dynamical Systems. A Series of Comprehensive Studies in Mathematics 260, Springer-Verlag. Zbl0522.60055MR722136
  7. Götze, F. ( 1991). Rate of convergence of simulated annealing processes. Préprint de l'Universität Bielefeld. MR1106283
  8. Holley, R. and Stroock, D. ( 1988). Simulated annealing via Sobolev inequalities. Communications in Mathematical Physics 115 553-569. Zbl0643.60092MR933455
  9. 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. Zbl0716.60073MR930082
  10. Mathieu, P. ( 1997). Hitting times and spectral gap inequalities. Annales de l'Institut Henri Poincaré 33 437-465. Zbl0894.60070MR1465797
  11. 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. Zbl0770.60090MR1231982
  12. 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. Zbl0882.60065MR1478710
  13. Mohar, B. ( 1989). Isoperimetric numbers of graphs. J. Comb. Theory B 47 274-291. Zbl0719.05042MR1026065
  14. 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. Zbl0602.58046MR841667
  15. 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. Zbl0885.60061MR1490046
  16. Trouvé, A. ( 1996). Cycle decompositions and simulated annealing. Society for Industrial and Applied Mathematics, Journal on Control and Optimization 34 966-986. Zbl0852.60031MR1384962
  17. 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. Zbl0853.60029MR1387393

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