We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the stan- dard tensorization property which holds in the independent case. As a corollary we obtain a family of dimensionless logarithmic Sobolev inequal- ities. In the context of spin systems on a graph, the weak dependence requirements resemble the well known Dobrushin uniqueness conditions. Our results can be considered as a discrete counterpart of a recent work of Katalin Marton [27]. We also discuss some natural generalizations such as approximate Shearer estimates and subadditivity of entropy.

Caputo, P., Menz, G., Tetali, P. (2015). Approximate tensorization of entropy at high temperature. ANNALES DE LA FACULTÉ DES SCIENCES DE TOULOUSE., 24(4), 691-716.

Approximate tensorization of entropy at high temperature

CAPUTO, PIETRO;
2015-01-01

Abstract

We show that for weakly dependent random variables the relative entropy functional satisfies an approximate version of the stan- dard tensorization property which holds in the independent case. As a corollary we obtain a family of dimensionless logarithmic Sobolev inequal- ities. In the context of spin systems on a graph, the weak dependence requirements resemble the well known Dobrushin uniqueness conditions. Our results can be considered as a discrete counterpart of a recent work of Katalin Marton [27]. We also discuss some natural generalizations such as approximate Shearer estimates and subadditivity of entropy.
2015
Caputo, P., Menz, G., Tetali, P. (2015). Approximate tensorization of entropy at high temperature. ANNALES DE LA FACULTÉ DES SCIENCES DE TOULOUSE., 24(4), 691-716.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/282758
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