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arXiv · 2607.14718

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

Sebastian Andres·Xin Chen·Martin Slowik·Kun Yin
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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 $L^{2}$-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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Sebastian Andres, Xin Chen, Martin Slowik, Kun Yin. 2026-07-16. Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps. https://arxiv.org/abs/2607.14718

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