Filippo Cesi
Quasi-factorization of the entropy and logarithmic Sobolev
inequalities for Gibbs random fields
(252K, PS)
ABSTRACT. We show that the entropy functional exhibits a quasi--factorization
property with respect to a pair of weakly dependent $\sigma$--algebras.
As an application we give a simple proof that the Dobrushin and Shlosman's
complete analyticity condition, for a Gibbs specification with finite range
summable interaction,
implies uniform logarithmic Sobolev inequalities.
This result has been previously proven using several different techniques.
The advantage of our approach is that it relies almost entirely on a
general property of the entropy, while very little is assumed
on the Dirichlet form. No topology is introduced on the
single spin space, thus discrete and continuous spins can be treated
in the same way.