Entropy-type inequalities for generalized Gamma densities

2019/09/30 by Toscani, Giuseppe · 1 citation
#35Q84 #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1909.13658

Abstract

We investigate the relaxation to equilibrium of the solution of a class of one-dimensional linear Fokker--Planck type equations that have been recently considered in connection with the study of addiction phenomena in a system of individuals. The steady states of these equations belong to the class of generalized Gamma densities. As a by-product of the relaxation analysis, we prove new weighted Poincaré and logarithmic Sobolev type inequalities for this class of densities.

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• Fokker--Planck equations and n--dimensional Poincaré inequalities for isotropic densities

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