The logarithmic Sobolev inequality for discrete spin systems on a lattice

作者: Daniel W. Stroock , Boguslaw Zegarlinski

DOI: 10.1007/BF02096629

关键词:

摘要: For finite range lattice gases with a finite spin space, it is shown that the Dobrushin-Shlosman mixing condition is equivalent to the existence of a logarithmic Sobolev inequality for the …

参考文章(17)
Roland Lvovich Dobrushin, Senya B Shlosman, None, Constructive Criterion for the Uniqueness of Gibbs Field Birkhäuser Boston. pp. 347- 370 ,(1985) , 10.1007/978-1-4899-6653-7_20
M. Aizenman, R. Holley, Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime Institute for Mathematics and Its Applications. ,vol. 8, pp. 1- 11 ,(1987) , 10.1007/978-1-4613-8734-3_1
Christian Maes, Senya B. Shlosman, Ergodicity of Probabilistic Cellular Automata: A Constructive Criterion Communications in Mathematical Physics. ,vol. 135, pp. 233- 251 ,(1991) , 10.1007/BF02098042
Sidney C. Port, Charles J. Stone, Infinite particle systems Transactions of the American Mathematical Society. ,vol. 178, pp. 307- 340 ,(1973) , 10.1090/S0002-9947-1973-0326868-3
Roland L Dobrushin, Senya B Shlosman, None, Completely Analytical Interactions: Constructive Description Journal of Statistical Physics. ,vol. 46, pp. 983- 1014 ,(1987) , 10.1007/BF01011153
Daniel W Stroock, Boguslaw Zegarlinski, The logarithmic Sobolev inequality for continuous spin systems on a lattice Journal of Functional Analysis. ,vol. 104, pp. 299- 326 ,(1992) , 10.1016/0022-1236(92)90003-2
Boguslaw Zegarlinski, On log-Sobolev inequalities for infinite lattice systems Letters in Mathematical Physics. ,vol. 20, pp. 173- 182 ,(1990) , 10.1007/BF00398360
Boguslaw Zegarlinski, Dobrushin uniqueness theorem and logarithmic Sobolev inequalities Journal of Functional Analysis. ,vol. 105, pp. 77- 111 ,(1992) , 10.1016/0022-1236(92)90073-R
Wayne G. Sullivan, A unified existence and ergodic theorem for Markov evolution of random fields Probability Theory and Related Fields. ,vol. 31, pp. 47- 56 ,(1974) , 10.1007/BF00538715
Daniel W. Stroock, Boguslaw Zegarlinski, The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition Communications in Mathematical Physics. ,vol. 144, pp. 303- 323 ,(1992) , 10.1007/BF02101094