Harnack inequalities on weighted graphs and some applications to the random conductance model

By S. Andres, Jean-Dominique Deuschel, Martin Slowik. 2013

56 citations recorded by the source corpus.

We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk $$X$$X in an environment of ergodic random conductances taking values in $$(0, \infty )$$(0,∞) satisfying some moment conditions.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2a97095ad83f0545672c4ad47e067e8bd7ef58d7

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In Mathematical Physics

1. S. Andres
2. Martin Slowik
3. Jean-Dominique Deuschel
4. Alberto Chiarini

In Statistics and Probability

1. Martin Slowik
2. Jean-Dominique Deuschel
3. S. Andres
4. Alberto Chiarini

Citations in the corpus

• Quenched invariance principle for random walks with time-dependent ergodic degenerate weights (2016, methodology): “In the case of static conductances, Moser iteration has already been implemented in order to show the QFCLT in [3], but also to obtain a local limit theorem and elliptic and parabolic Harnack inequalities in [4] as well as upper Gaussian estimates on the heat kernel in [5].”
• Invariance principle for the random conductance model in a degenerate ergodic environment (2013, methodology): “Finally, in [3], we will apply the adaptations of the Moser iteration technique in this work to derive both elliptic and parabolic Harnack inequalities under the assumptions of Theorem 1.”