Optimal heat kernel bounds under logarithmic Sobolev inequalities

Bakry, Dominique, Concordet, Daniel, and Ledoux, Michel. "Optimal heat kernel bounds under logarithmic Sobolev inequalities." ESAIM: Probability and Statistics 1 (2010): 391-407. <http://eudml.org/doc/197731>.

@article{Bakry2010,
abstract = { 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. },
author = {Bakry, Dominique, Concordet, Daniel, Ledoux, Michel},
journal = {ESAIM: Probability and Statistics},
keywords = {heat kernel / logarithmic Sobolev inequality / entropy-energy inequality / best constant / off-diagonal estimates / non-negative Ricci curvature.; Riemannian manifold; functional inequalities; Markov semigroups; optimal uniform upper estimates; heat kernels; logarithmic Sobolev inequality; entropy-energy inequality; diffusion operators},
language = {eng},
month = {3},
pages = {391-407},
publisher = {EDP Sciences},
title = {Optimal heat kernel bounds under logarithmic Sobolev inequalities},
url = {http://eudml.org/doc/197731},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Bakry, Dominique
AU - Concordet, Daniel
AU - Ledoux, Michel
TI - Optimal heat kernel bounds under logarithmic Sobolev inequalities
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 391
EP - 407
AB - 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.
LA - eng
KW - heat kernel / logarithmic Sobolev inequality / entropy-energy inequality / best constant / off-diagonal estimates / non-negative Ricci curvature.; Riemannian manifold; functional inequalities; Markov semigroups; optimal uniform upper estimates; heat kernels; logarithmic Sobolev inequality; entropy-energy inequality; diffusion operators
UR - http://eudml.org/doc/197731
ER -