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Article Dans Une Revue Electronic Communications in Probability Année : 2015

A lower bound on the relative entropy with respect to a symmetric probability

Matthias Gorny
  • Fonction : Auteur

Résumé

Let ρ and µ be two probability measures on R which are not the Dirac mass at 0. We denote by H(µ|ρ) the relative entropy of µ with respect to ρ. We prove that, if ρ is symmetric and µ has a finite first moment, then H(µ|ρ) ≥ R z dµ(z) 2 2 R z 2 dµ(z) , with equality if and only if µ = ρ. We give an applicaion to the Curie-Weiss model of self-organized criticality.
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Dates et versions

hal-03827283 , version 1 (24-10-2022)

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Citer

Raphaël Cerf, Matthias Gorny. A lower bound on the relative entropy with respect to a symmetric probability. Electronic Communications in Probability, 2015, 20 (none), ⟨10.1214/ECP.v20-3920⟩. ⟨hal-03827283⟩
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