Quenched local limit theorem for random conductance models with long-range jumps
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914747536900096 |
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| author | Chen, Xin Kumagai, Takashi Wang, Jian |
| author_facet | Chen, Xin Kumagai, Takashi Wang, Jian |
| contents | We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack inequalities and on-diagonal heat-kernel estimates for long-range random walks on general ergodic environments. In particular, this partly solves \cite[Open Problem 2.7]{BCKW}, where the quenched invariance principle was obtained. As a byproduct, we prove the maximal inequality with an extra tail term for long-range reversible random walks, which in turn yields the everywhere sublinear property for the associated corrector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quenched local limit theorem for random conductance models with long-range jumps Chen, Xin Kumagai, Takashi Wang, Jian Probability We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack inequalities and on-diagonal heat-kernel estimates for long-range random walks on general ergodic environments. In particular, this partly solves \cite[Open Problem 2.7]{BCKW}, where the quenched invariance principle was obtained. As a byproduct, we prove the maximal inequality with an extra tail term for long-range reversible random walks, which in turn yields the everywhere sublinear property for the associated corrector. |
| title | Quenched local limit theorem for random conductance models with long-range jumps |
| topic | Probability |
| url | https://arxiv.org/abs/2402.07212 |