WIAS Preprint No. 3017, (2023)

Quenched homogenization of infinite range random conductance model on stationary point processes



Authors

  • Bokredenghel, Yonas
  • Heida, Martin
    ORCID: 0000-0002-7242-8175

2020 Mathematics Subject Classification

  • 60H25 60K37 35B27 35R60 47B80 47A75

Keywords

  • Random conductance model, stochastic homogenization, optimal conditions, compactness

DOI

10.20347/WIAS.PREPRINT.3017

Abstract

We prove homogenization for elliptic long-range operators in the random conductance model on random stationary point processes in d dimensions with Dirichlet boundary conditions and with a jointly stationary coefficient field. Doing so, we identify 4 conditions on the point process and the coefficient field that have to be fulfilled at different stages of the proof in order to pass to the homogenization limit. The conditions can be clearly attributed to concentration of support, Rellich--Poincaré inequality, non-degeneracy of the homogenized matrix and ergodicity of the elliptic operator.

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