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Optimal heat kernel bounds under logarithmic Sobolev inequalities

Dominique BakryDaniel ConcordetMichel Ledoux — 2010

ESAIM: Probability and Statistics

We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators of the type Laplacian minus the gradient of a smooth potential with a given growth at infinity....

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