Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps

2026/07/16 by Sebastian Andres, Xin Chen, Martin Slowik +1
#math.PR #math.AP

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Abstract

We show anchored versions of the Nash inequality for discrete non-local divergence-form operators with degenerate weights. They allow to control the L²-norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide on-diagonal heat kernel upper bounds for a class of random conductance models with degenerate jump rates allowing long-range jumps. The results are established on a class of graphs including the integer lattice and possibly correlated supercritical percolation clusters.

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