Precise estimates on the rate at which certain diffusions tend to equilibrium.

L. Saloff-Coste

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Optimal heat kernel bounds under logarithmic Sobolev inequalities

Dominique Bakry, Daniel Concordet, Michel Ledoux (2010)

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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...