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Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments

Abstract : We introduce anchored versions of the Nash inequality. They allow to control the L 2 norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide heat kernel upper bounds for diffusions in degenerate static and dynamic random environments. As an example, we apply our results to the case of a random walk with degenerate jump rates that depend on an underlying exclusion process at equilibrium.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01401897
Contributor : Jean-Christophe Mourrat <>
Submitted on : Wednesday, November 23, 2016 - 10:39:49 PM
Last modification on : Wednesday, November 20, 2019 - 8:08:20 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 6:44:17 AM

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Jean-Christophe Mourrat, Felix Otto. Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments. Journal of Functional Analysis, Elsevier, 2016, 270, pp.201 - 228. ⟨10.1016/j.jfa.2015.09.020⟩. ⟨ensl-01401897⟩

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