Hydrodynamics for the partial exclusion process in random environment
| Autor: | Frank Redig, Simone Floreani, Federico Sau |
|---|---|
| Přispěvatelé: | Floreani, S., Redig, F., Sau, F. |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Arbitrary starting point quenched invariance principle Duality 01 natural sciences Homogenization (chemistry) 010104 statistics & probability Random conductance model Random environment FOS: Mathematics Mild solution Hydrodynamic limit Path space Statistical physics 0101 mathematics Mathematics Particle system Invariance principle Applied Mathematics 010102 general mathematics Ergodicity Probability (math.PR) Conductance Modeling and Simulation Mathematics - Probability |
| Zdroj: | Stochastic Processes and their Applications, 142 |
| ISSN: | 0304-4149 |
| Popis: | In this paper, we introduce a random environment for the exclusion process in $\mathbb{Z}^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in [39] and [21]. To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in [40]. Comment: 34 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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