# Optimal heat kernel bounds under logarithmic Sobolev inequalities

Dominique Bakry; Daniel Concordet; Michel Ledoux

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 391-407
- ISSN: 1292-8100

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topBakry, 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 -

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