Some drawbacks of finite modified logarithmic Sobolev inequalities
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Laurent Miclo [1]
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[1] Paul Sabatier University
Paul Sabatier University
Arrondissement de Toulouse, Francia
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- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 123, Nº 1, 2018, págs. 147-159
- Idioma: inglés
- DOI: 10.7146/math.scand.a-105279
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Resumen
Classically, finite modified logarithmic Sobolev inequalities are used to deduce a differential inequality for the evolution of the relative entropy with respect to the invariant measure. We will check that these inequalities are ill-behaved with respect, on one hand, to the symmetrization procedure, and on the other hand, to the umbrella sampling procedure for Poincaré inequalities. A short spectral proof of the latter method is given to estimate the spectral gap of a finite reversible Markov generator L in terms of the spectral gap of the restrictions of L on two subsets whose union is the whole state space and whose intersection is not empty.
