A note on heat kernel estimates on weighted graphs with two-sided bounds on the weights.

Schmidt, Andreas U.

Displaying similar documents to “A note on heat kernel estimates on weighted graphs with two-sided bounds on the weights.”

A geometric approach to on-diagonal heat kernel lower bounds on groups

Thierry Coulhon, Alexander Grigor&#039;yan, Christophe Pittet (2001)

Annales de l’institut Fourier

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We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath...

Random walk on graphs with regular resistance and volume growth

András Telcs (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space–time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

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We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays

Thierry Coulhon (1998)

Journées équations aux dérivées partielles

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In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of $L^{2}$ isoperimetric profile. The main point is to connect the decay of the $L^{1} - L^{\infty}$ norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods....