Erasure Entropies and Gibbs Measures

#### E.A. Verbitskiy, A.C.D. van Enter

2010, v.16, Issue 1, 3-14

ABSTRACT

Recently Verdu and Weissman introduced erasure entropies, which are meant to measure the information carried by one or more symbols given all of the remaining symbols in the realization of a random process or field. A natural relation to Gibbs measures has also been observed. In this short note we study this relation further, review a few earlier contributions from statistical mechanics, and provide the formula for the erasure entropy of a Gibbs measure in terms of the corresponding potential. For some 2-dimensional Ising models, for which Verdu and Weissman suggested a numerical procedure, we show how to obtain an exact formula for the erasure entropy.

Keywords: erasure entropy,Gibbs measures,solvable Ising models,conditional entropy