Quenched local limit theorem for a directed random walk on the backbone of a supercritical oriented percolation cluster for $d \ge 1$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908747998167040 |
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| author | Bethuelsen, Stein Andreas Birkner, Matthias Depperschmidt, Andrej Schlüter, Timo |
| author_facet | Bethuelsen, Stein Andreas Birkner, Matthias Depperschmidt, Andrej Schlüter, Timo |
| contents | In this work we extend the quenched local limit theorem obtained by the authors in [BBDS23]. More precisely, we consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with $d\geq 1$ being the spatial dimension. In [BBDS23] an annealed local central limit theorem was proven for all $d\geq 1$ and a quenched local limit theorem under the assumption $d\geq 3$. Here we show that the latter result also holds for all $d \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quenched local limit theorem for a directed random walk on the backbone of a supercritical oriented percolation cluster for $d \ge 1$ Bethuelsen, Stein Andreas Birkner, Matthias Depperschmidt, Andrej Schlüter, Timo Probability 60K37, 60J10, 82B43, 60K35 In this work we extend the quenched local limit theorem obtained by the authors in [BBDS23]. More precisely, we consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with $d\geq 1$ being the spatial dimension. In [BBDS23] an annealed local central limit theorem was proven for all $d\geq 1$ and a quenched local limit theorem under the assumption $d\geq 3$. Here we show that the latter result also holds for all $d \ge 1$. |
| title | Quenched local limit theorem for a directed random walk on the backbone of a supercritical oriented percolation cluster for $d \ge 1$ |
| topic | Probability 60K37, 60J10, 82B43, 60K35 |
| url | https://arxiv.org/abs/2410.14302 |