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Stationary measures of stochastic gradient systems, infinite lattice models. (English) Zbl 0465.60088


MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
Full Text: DOI

References:

[1] Doss, H.; Royer, G., Processus de diffusion associé aux mesures de Gibbs sur \(\mathbb{R}^{\mathbb{Z}^d } \), Z. Wahrscheinlichkeitstheorie verw. Gebiete, 46, 107-124 (1978) · Zbl 0377.60090
[2] Fritz, J., An information-theoretical proof of limit theorems for reversible Markov processes, Trans. Sixth Prague Conference Information Theory, Stat. Decision Functions, Random Processes 1971, 183-197 (1973), Prague: Czechoslovak Academy Publishing House, Prague · Zbl 0282.60038
[3] Fritz, J.: In one and two dimensions formally invariant measures are Gibbsian, Continuous spin models of first order. Technical Report, 1979
[4] Fritz, J., Infinite lattice systems of interacting diffusion processes, Existence and regularity properties, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 59, 291-309 (1982) · Zbl 0458.60096
[5] Holley, R., Free energy in a Markovian model of a lattice spin system, Commun. math. Phys., 23, 87-99 (1971) · Zbl 0241.60096
[6] Holley, R.; Stroock, D., In one and two dimensions every stationary mesure for a stochastic Ising model is a Gibbs state, Commun. math. Phys., 55, 37-45 (1977)
[7] Holley, R., Stroock, D.: Diffusions on an infinite dimensional torus. J. Functional Analysis (In press) · Zbl 0501.58039
[8] Rényi, A., On measures of entropy and information, Proc. 4th Berkeley Sympos. Math. Statist. Probab., Vol. I, 547-561 (19601961), Berkeley-Los Angeles: Univ. California Press, Berkeley-Los Angeles · Zbl 0106.33001
[9] Royer, G., Processus de diffusion associé à certains modèles d’Ising à spin continus, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 46, 163-176 (1979) · Zbl 0377.60088
[10] Stein, E. M., Singular Integrals and Differentiability Properties of Functions (1970), Princeton: Princeton Univ. Press, Princeton · Zbl 0207.13501
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