From quenched invariance principle to semigroup convergence with applications to exclusion processes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909946823573504 |
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| author | Chiarini, Alberto Floreani, Simone Sau, Federico |
| author_facet | Chiarini, Alberto Floreani, Simone Sau, Federico |
| contents | Consider a random walk on $\mathbb{Z}^d$ in a translation-invariant and ergodic random environment and starting from the origin. In this short note, assuming that a quenched invariance principle for the opportunely-rescaled walks holds, we show how to derive an $L^1$-convergence of the corresponding semigroups. We then apply this result to obtain a quenched pathwise hydrodynamic limit for the simple symmetric exclusion process on $\mathbb{Z}^d$, $d\ge 2$, with i.i.d. symmetric nearest-neighbors conductances $ω_{xy}\in [0,\infty)$ only satisfying $$\mathbb{Q}(ω_{xy}>0)>p_c\ ,$$ where $p_c$ is the critical value for bond percolation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04127 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From quenched invariance principle to semigroup convergence with applications to exclusion processes Chiarini, Alberto Floreani, Simone Sau, Federico Probability Mathematical Physics 60K35, 60K37, 60G22, 35B27, 60F17, 82C41, 82B43 Consider a random walk on $\mathbb{Z}^d$ in a translation-invariant and ergodic random environment and starting from the origin. In this short note, assuming that a quenched invariance principle for the opportunely-rescaled walks holds, we show how to derive an $L^1$-convergence of the corresponding semigroups. We then apply this result to obtain a quenched pathwise hydrodynamic limit for the simple symmetric exclusion process on $\mathbb{Z}^d$, $d\ge 2$, with i.i.d. symmetric nearest-neighbors conductances $ω_{xy}\in [0,\infty)$ only satisfying $$\mathbb{Q}(ω_{xy}>0)>p_c\ ,$$ where $p_c$ is the critical value for bond percolation. |
| title | From quenched invariance principle to semigroup convergence with applications to exclusion processes |
| topic | Probability Mathematical Physics 60K35, 60K37, 60G22, 35B27, 60F17, 82C41, 82B43 |
| url | https://arxiv.org/abs/2303.04127 |