Summary
We study the asymptotic behaviour of random products of Ruelle-Perron-Frobenius operators. We extend the previous work of Ruelle in the homogeneous case to the random case.
Résumé
Nous étudions le comportement asymptotique de produits aléatoires d'opérateurs de Ruelle-Perron-Frobenius. Nous étendons le travail de Ruelle obtenu dans le cas homogène, au cas aléatoire.
Bibliographie
Birkhoff, G.: Extensions of Jentzsch's theorem. Trans. Am. Math. Soc. 85, 219–227 (1957)
Birkhoff, G.: Lattice theory, 3rd. edn., Amer. Math. Soc. 1967)
Bowen, R.: Equilibrium spaces and the ergodic theory of Anosov diffeomorphisms. Lect. Notes Math. vol. 470. Berlin Heidelberg New York: Springer 1975
Derrienic, Y.: Sur le theorème ergodique sous-additif. C.R. Acad. Sci. 281A, 985–988 (1975)
Evstigneev, I.V.: Positive matrix-valued cocycles over dynamical systems. Uspehi Math. Nauk. 29, 219–226 (1974)
Furstenberg, H., Kesten, H.: Products of random matrices. Ann. Math. Statist. 31, 457–469 (1960)
Ferrero, P.: Thèse CPT 81/P 1277. Université de Marseille 1981
Keane, M.: Strongly mixing g-measures. Invent. Math. 16, 309–324 (1972)
Ledrappier, F.: Principe variationnel et systèmes dynamiques symboliques. Z. Wahrscheinlichkeitstheor. Verw. Geb. 30, 185–202 (1974)
Ledrappier, F., Walters, P.: A relativised variational principle for continuous transformations. J. Lond. Math. Soc. 16, 568–576 (1977)
Rohlin, V.A.: Lectures on the entropy theory of measure preserving transformations. Russ. Math. Surv. 22, 1–52 (1968)
Ruelle, D.: Statistical mechanics of a one dimensional lattice gas. Commun. Math. Phys. 9, 267–278 (1968)
Ruelle, D.: A measure associated with axiome A attractors. Am. J. Math. 98, 619–654 (1976)
Ruelle, D.: Thermodynamic formalism. New-York: Addision-Wesley 1978
Walters, P.: Invariant measure and equilibrium states for some mappings which e pand distances. Trans. Am. Math. Soc. 236, 121–153 (1978)
Walters, P.: Ruelle's operator theorem and g-measures. Trans. Am. Math. Soc. 214, 375–387 (1975)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ferrero, P., Schmitt, B. Produits aléatoires d'opérateurs matrices de transfert. Probab. Th. Rel. Fields 79, 227–248 (1988). https://doi.org/10.1007/BF00320920
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00320920