Logarithmic Sobolev inequalities and stochastic Ising models. (English) Zbl 0682.60109

Summary: We use logarithmic Sobolev inequalities to study the ergodic properties of stochastic Ising models both in terms of large deviations and in terms of convergence in distribution.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
Full Text: DOI


[1] E. A. Carlen and D. W. Stroock, An application of the Bakry-Emery criterion to infinite dimensional diffusions, to appear. · Zbl 0609.60086
[2] L. Clemens, Ph.D. thesis, MIT, Cambridge, Massachusetts.
[3] J. Glemm, Boson fields with non-linear self-interactions in two dimensions,Commun. Math. Phys. 8:12-25 (1968). · Zbl 0173.29903 · doi:10.1007/BF01646421
[4] L. Gross, Logarithmic Sobolev inequalities,Am. J. Math. 97:1061-1083 (1976). · Zbl 0318.46049 · doi:10.2307/2373688
[5] R. Holley, Convergence inL2 of stochastic Ising models: Jump processes and diffusions, inProceedings of the Tanaguchi International Symposium on Stochastic Analysis at Katata, 1982 (North-Holland, 1984) pp. 149-167.
[6] R. Holley, Rapid convergence to equilibrium in one-dimensional stochastic Ising models,Ann. Prob. 13:72-89 (1985). · Zbl 0558.60077 · doi:10.1214/aop/1176993067
[7] R. Holley and D. W. Stroock, Applications of the stochastic Ising model to the Gibbs states,Commun. Math. Phys. 48:249-265 (1976). · doi:10.1007/BF01617873
[8] R. Holley and D. W. Stroock,L 2 theory of the stochastic Ising model,Z. Wahr. Verw. Geb. 35:87-101 (1976). · Zbl 0332.60073 · doi:10.1007/BF00533313
[9] R. Holley and D. W. Stroock, Diffusions on an infinite dimensional torus,J. Funct. Anal. 42:29-63 (1981). · Zbl 0501.58039 · doi:10.1016/0022-1236(81)90047-1
[10] O. S. Rothaus, Diffusions in compact Riemannian manifolds and logarithmic Sobolev inequalities,J. Fund. Anal. 42:102-109 (1981). · Zbl 0471.58027 · doi:10.1016/0022-1236(81)90049-5
[11] D. Ruelle,Statistical Mechanics (Benjamin, New York, 1969).
[12] D. Stroock,An Introduction to the Theory of Large Deviations (Universitext, Springer-Verlag, New York, 1984). · Zbl 0552.60022
[13] D. Stroock, to appear.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.