Moment bounds on correctors for the degenerate random conductance model

TL;DR

This paper derives sharp bounds on the spatial growth of correctors in the degenerate random conductance model on , linking their stochastic integrability to that of the conductances, under spectral-gap assumptions.

Contribution

It provides the first moment bounds on correctors for degenerate conductance models with unbounded conductances, extending previous results to more general settings.

Findings

Established sharp bounds on correctors' spatial growth.

Quantified the relation between correctors' integrability and conductances.

Extended moment bounds to degenerate, unbounded conductance scenarios.

Abstract

We study the random conductance model on the lattice $\Z^d$, i.e. we consider a linear, finite-difference, divergence-form operator with random conductances $a$. We allow the conductances $a$ to be unbounded and degenerate. Assuming the conductances satisfy a spectral-gap inequality, we establish sharp bounds on the spatial growth of correctors, together with a quantitative relation between the stochastic integrability of the correctors and that of $a$.