Gaussian maximum of entropy and reversed log-Sobolev inequality
Binomial-Poisson entropic inequalities and the M/M/ queue
This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/ queue. They describe in particular the exponential dissipation of -entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group ...
On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities
Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter of the mixed...
Page 1