A Priori Estimates for Symmetrizing Measures and Their Applications to Gibbs States

Journal of Functional Analysis

Volumn 171, Issue 2, 2000, Pages 366-400

  Albeverio, S ^a,b,c   Kondratiev, Yu G ^a   Rockner M ^b,d   Tsikalenko, T V ^d,e  

^a UNIVERSITY OF BONN   (Germany)

^b BiBoS Research Centre Bielefeld   (Germany)

^c CERFIM   (Switzerland)

^d BIELEFELD UNIVERSITY   (Germany)

^e INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034628712     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3482     Document Type: Article

References (34)

1. Albeverio S., Bogachev V. I., Röckner M. On uniqueness of invariant measures for finite and infinite dimensional diffusions. Comm. Pure Appl. Math. 52:1999;325-362.
2. Albeverio S., Høegh-Krohn R. Homogeneous random fields and quantum statistical mechanics. J. Funct. Anal. 19:1975;241-272.
3. Albeverio S., Kondratiev Yu. G., Röckner M. Dirichlet operators via stochastic analysis. J. Funct. Anal. 128:1995;102-138.
4. 2-semigroups and extremality of Gibbs states. J. Funct. Anal. 144:1997;394-423.
5. Albeverio S., Kondratiev Yu. G., Röckner M. Ergodicity of the stochastic dynamics of quasi-invariant measures and applications to Gibbs states. J. Funct. Anal. 149:1997;415-469.
6. Albeverio S., Kondratiev Yu. G., Röckner M., Tsikalenko T. V. Uniqueness of Gibbs states for quantum lattice systems. Prob. Theory Related Fields. 108:1997;193-218.
7. Albeverio S., Kondratiev Yu. G., Röckner M., Tsikalenko T. V. A-priori estimates and existence of Gibbs measures: a simplified proof. C. R. Acad. Sci. Paris Sér. I. 328:1999;1049-1054.
8. Albeverio S., Röckner M. Classical Dirichlet forms on topological vector spaces - Closability and a Cameron-Martin formula. J. Funct. Anal. 88:1990;395-436.
9. Albeverio S., Röckner M. Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms. Probab. Theory Related Fields. 89:1991;347-386.
10. Bell D. A quasi-invariance theorem for measures on Banach spaces. Trans. Amer. Math. Soc. 290:1985;851-855.
11. Bellissard J., Høegh-Krohn R. Compactness and the maximal Gibbs states for random Gibbs fields on a lattice. Comm. Math. Phys. 84:1982;297-327.
12. Berezansky Yu. M., Kondratiev Yu. G. Spectral Methods in Infinite Dimensional Analysis. 1993;Kluwer Academic, Dordrecht.
13. Bogachev V. I. Differential measures and the Malliavin calculus. J. Math. Sci. 87:1997;3577-3731.
14. Bogachev V. I., Röckner M. Regularity of invariant measures on finite and infinite dimensional spaces and applications. J. Funct. Anal. 133:1995;168-223.
15. Cassandro M., Olivieri E., Pellegrinotti A., Presutti E. Existence and uniqueness of DLR measures for unbounded spin systems. Z. Wahrsch. Verw. Gebiete. 41:1978;313-334.
16. Daletskii Yu. L., Fomin S. V. Measures and Differential Equations in Infinite Dimensions. 1991;Kluwer Academic, Dordrecht.
17. Dobrushin R. L. The description of a random field by means of conditional probabilities and conditions of its regularity. Theory Probab. Appl. 13:1968;197-224.
18. Dobrushin R. L. Prescribing a system of random variables by conditional distributions. Theory Probab. Appl. 15:1970;458-486.
19. Da Prato G., Zabczyk J. Convergence to equilibrium for classical and quantum spin systems. Probab. Theory Related Fields. 103:1995;529-552.
20. Daletskii Yu. L., Sokhadze G. A. Absolute continuity of smooth measures. Funct. Anal. Appl. 22:1988;149-150.
21. Föllmer H. A covariance estimate for Gibbs measures. J. Funct. Anal. 46:1982;387-395.
22. Föllmer H. Random fields and diffusion processes. Lecture Notes Math. 1988;Springer-Verlag, Berlin/New York. p. 101-204.
23. Fritz J. Stationary measures of stochastic gradient dynamics, infinite lattice models. Z. Wahrsch. Verw. Gebiete. 59:1982;479-490.
24. Georgii H.-O. Gibbs Measures and Phase Transitions. Studies in Mathematics. 9:1988;de Gruyter, Berlin/New York.
25. Gross L. Decay of correlations in classical lattice models at high temperature. Comm. Math. Phys. 68:1979;9-27.
26. 2-theory for the stochastic Ising model. Z. Wahrsch. Verw. Gebiete. 35:1976;87-101.
27. Kirillov A. I. On the reconstruction of measures from their logarithmic derivatives. Izv. Ross. Akad. Nauk Ser. Mat. 59:1995;121-138.
28. Lebowitz J. L., Presutti E. Statistical mechanics of systems of unbounded spins. Comm. Math. Phys. 50:1976;195-218.
29. Preston C. Random Fields. Lecture Notes in Math. 534:1976;Springer-Verlag, Berlin/New York.
30. C. Preston, Specifications and their Gibbs states, preprint, Universität Bielefeld, 1998.
31. γ. J. Math. Pures Appl. 56:1977;455-478.
32. Sinai Ya. Theory of Phase Transitions: Rigorous Results. 1982;Pergamon, Oxford.
33. Skorohod A. V. Integration on Hilbert Space. 1984;Springer-Verlag, Berlin/New York.
34. Zegarlinski B. The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice. Comm. Math. Phys. 175:1996;401-432.