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

2015/03/28 by Jean-Christophe Mourrat, Félix Otto, Mourrat, Jean-Christophe +1 · 1 citation
Mathematics · #26D10 #35B65 #35K65 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1503.08280

openalex publication_date 2015/03/28 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28

Abstract

We introduce anchored versions of the Nash inequality. They allow to control\nthe L² norm of a function by Dirichlet forms that are not uniformly\nelliptic. We then use them to provide heat kernel upper bounds for diffusions\nin degenerate static and dynamic random environments. As an example, we apply\nour results to the case of a random walk with degenerate jump rates that depend\non an underlying exclusion process at equilibrium.\n

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