On quenched homogenization of long-range random conductance models on stationary ergodic point processes
- Heida, Martin
2020 Mathematics Subject Classification
- 60H25 60K37 35B27 35R60 47B80 47A75
- Random conductance model, stochastic homogenization, Rellich, Poincaré
We study the homogenization limit on bounded domains for the long-range random conductance model on stationary ergodic point processes on the integer grid. We assume that the conductance between neares neighbors in the point process are always positive and satisfy certain weight conditions. For our proof we use long-range two-scale convergence as well as methods from numerical analysis of finite volume methods.