An ergodic theorem with weights and applications to random measures, RW homogenization and IPS hydrodynamics on point processes
| Autor: | Faggionato, A. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove a multidimensional ergodic theorem with weighted averages for the action of the group $\mathbb{Z}^d$ on a probability space. At level $n$ weights are of the form $n^{-d} \psi(j/n)$, $ j\in \mathbb{Z}^d$, for real functions $\psi$ decaying suitably fast. We discuss applications to random measures and to quenched stochastic homogenization of random walks on simple point processes with long-range random jump rates, allowing to remove the technical Assumption (A9) from \cite[Theorem~4.4]{Fhom1}. This last result concerns also some semigroup and resolvent convergence particularly relevant for the derivation of the quenched hydrodynamic limit of interacting particle systems via homogenization and duality. As a consequence we show that also the quenched hydrodynamic limit of the symmetric simple exclusion process on point processes stated in \cite[Theorem~4.1]{F_SEP} remains valid when removing the above mentioned Assumption (A9). Comment: To appear in the special issue of SPA in memory of Francis Comets. 35 pages, 2 figures. The presentation is now self-contained and with additional examples |
| Databáze: | arXiv |
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