Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Stability of parabolic Harnack inequalities


Code(s) de Classification MSC:

Résumé: Let $(G,E)$ be a graph with weights $\{a_{xy}\}$ for which a parabolic Harnack inequality holds with space-time scaling exponent $\beta\ge 2$. Suppose $\{a'_{xy}\}$ is another set of weights that are comparable to $\{a_{xy}\}$. We prove that this parabolic Harnack inequality also holds for $(G,E)$ with the weights $\{a'_{xy}\}$. We also give necessary and sufficient conditions for this parabolic Harnack inequality to hold.

Mots Clés: Harnack inequality ; random walks on graphs ; volume doubling ; Green functions ; Poincaré inequality ; Sobolev inequality ; anomalous diffusion

Date: 2002-06-05

Prépublication numéro: PMA-736

Pdf file : PMA-736.pdf