Hydrodynamic limit of simple exclusion processes in symmetric random environments via duality and homogenization

Autor: Alessandra Faggionato
Rok vydání: 2022
Předmět:
Zdroj: Probability Theory and Related Fields volume
ISSN: 0178-8051
DOI: 10.1007/s00440-022-01163-8
Popis: We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above randomness is left invariant by the action of the group $\mathbb{G}=\mathbb{R}^d$ or $\mathbb{G}=\mathbb{Z}^d$. We then add a site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits a hydrodynamic limit in path space. The hydrodynamic equation is non-random and governed by the effective homogenized matrix $D$ of the single random walk, which can be degenerate. The above result covers a very large family of models including e.g. simple exclusion processes built from random conductance models on $\mathbb{Z}^d$ and on crystal lattices (possibly with long conductances), Mott variable range hopping, simple random walks on Delaunay triangulations, random walks on supercritical percolation clusters.
Comment: 43 pages. Minor corrections and extensions. Extended Section 5 with further applications. Added new Appendix A with an example of degenerate nonzero effective homogenized matrix
Databáze: OpenAIRE
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