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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J27 Markov chains with continuous parameter
- 60J35 Transition functions, generators and resolvents, See Also {47D03, 47D07}
- 31B05 Harmonic, subharmonic, superharmonic functions

**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