Erasure entropies and Gibbs measures


Recently Verdù 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 2dimensional Ising models, for which Verdú and Weissman suggested a numerical proedure, we show how to obtain an exact formula for the erasure entropy.

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@article{Enter2010ErasureEA, title={Erasure entropies and Gibbs measures}, author={Aernout van Enter and Evgeny Verbitskiy}, journal={CoRR}, year={2010}, volume={abs/1001.3122} }