scholarly journals Logarithmic Sobolev Inequalities for Unbounded Spin Systems Revisited

2001 ◽  
pp. 167-194 ◽  
Author(s):  
M. Ledoux
Keyword(s):  
Spin Systems ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities ◽  
Unbounded Spin Systems ◽  
Unbounded Spin

scholarly journals Entropy inequalities for unbounded spin systems

2002 ◽  
Vol 30 (4) ◽  
pp. 1959-1976 ◽  
Author(s):  
Paolo Dai Pra ◽  
Anna Maria Paganoni ◽  
Gustavo Posta
Keyword(s):  
Spin Systems ◽  
Unbounded Spin Systems ◽  
Entropy Inequalities ◽  
Unbounded Spin

Existence and uniqueness of DLR measures for unbounded spin systems

1978 ◽  
Vol 41 (4) ◽  
pp. 313-334 ◽  
Author(s):  
M. Cassandro ◽  
E. Olivieri ◽  
A. Pellegrinotti ◽  
E. Presutti
Keyword(s):  
Existence And Uniqueness ◽  
Spin Systems ◽  
Unbounded Spin Systems ◽  
Unbounded Spin

scholarly journals Clustering Bounds on n-Point Correlations for Unbounded Spin Systems

2009 ◽  
Vol 136 (3) ◽  
pp. 405-452 ◽  
Author(s):  
Abdelmalek Abdesselam ◽  
Aldo Procacci ◽  
Benedetto Scoppola
Keyword(s):  
Spin Systems ◽  
Unbounded Spin Systems ◽  
Unbounded Spin

scholarly journals CONCENTRATION INEQUALITIES FOR GIBBS MEASURES

2011 ◽  
Vol 14 (01) ◽  
pp. 79-104
Author(s):  
IOANNIS PAPAGEORGIOU
Keyword(s):  
Gibbs Measures ◽  
Type Inequality ◽  
Sobolev Type ◽  
Sobolev Inequalities ◽  
Infinite Dimensional ◽  
Unbounded Spin Systems ◽  
The One ◽  
Concentration Properties ◽  
Weaker Conditions ◽  
Unbounded Spin

We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a quadratic. At first we assume that the one-site measure satisfies a modified log-Sobolev inequality with a constant uniformly on the boundary conditions and we determine conditions so that the infinite-dimensional Gibbs measure satisfies a concentration as well as a Talagrand type inequality, similar to the ones obtained by Barthe and Roberto6 for the product measure. Then a modified log-Sobolev type concentration property is obtained under weaker conditions referring to the log-Sobolev inequalities for the boundary free measure.

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