The log-Sobolev inequality for weakly coupled lattice fields

被引：31

作者：

Yoshida, N ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Sci, Div Math, Kyoto 6068502, Japan

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1999年 / 115卷 / 01期

关键词：

D O I：

10.1007/s004400050235

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a ferromagnetic spin system with unbounded interactions on the d-dimensional integer lattice (d greater than or equal to 1). Under mild assumptions on the one-body interactions (so that arbitrarily deep double wells are allowed), we prove that if the coupling constants are small enough, then the finite volume Gibbs states satisfy the log-Sobolev inequality uniformly in the volume and the boundary condition. Mathematics Subject Classification (1991): 60K35, 82B20.

引用

页码：1 / 40

页数：40

共 50 条

[1] The log-Sobolev inequality for weakly coupled lattice fields
Nobuo Yoshida
Probability Theory and Related Fields, 1999, 115 : 1 - 40
[2] A Note on the Modified Log-Sobolev Inequality
Ioannis Papageorgiou
Potential Analysis, 2011, 35 : 275 - 286
[3] The log-Sobolev inequality with quadratic interactions
Papageorgiou, Ioannis
JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (08)
[4] A Note on the Modified Log-Sobolev Inequality
Papageorgiou, Ioannis
POTENTIAL ANALYSIS, 2011, 35 (03) : 275 - 286
[5] Log-Sobolev inequality for the multislice, with applications
Filmus, Yuval
O'Donnell, Ryan
Wu, Xinyu
ELECTRONIC JOURNAL OF PROBABILITY, 2022, 27 : 1 - 30
[6] Log-Sobolev inequality for the φ24 and φ34 measures
Bauerschmidt, Roland
Dagallier, Benoit
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2024, 77 (05) : 2579 - 2612
[7] The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
Yoshida, N
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (02): : 223 - 243
[8] The Log-Sobolev inequality for unbounded spin systems
Bodineau, T
Helffer, B
JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 166 (01) : 168 - 178
[9] Optimal integrability condition for the log-Sobolev inequality
Chen, Xin
Wang, Feng-Yu
QUARTERLY JOURNAL OF MATHEMATICS, 2007, 58 : 17 - 22
[10] ON LOG-SOBOLEV INEQUALITIES FOR INFINITE LATTICE SYSTEMS
ZEGARLINSKI, B
LETTERS IN MATHEMATICAL PHYSICS, 1990, 20 (03) : 173 - 182

← 1 2 3 4 5 →