Small ball probabilities for the passage time in planar first-passage percolation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916794547044352 |
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| author | Elboim, Dor |
| author_facet | Elboim, Dor |
| contents | We study planar first-passage percolation with independent weights whose common distribution is supported in $(0,\infty)$ and is absolutely continuous with respect to Lebesgue measure. We prove that the passage time from $x$ to $y$ denoted by $T(x,y)$ satisfies $$\max _{a\ge 0} \mathbb P \big( T(x,y)\in [a,a+1] \big) \le \frac{C}{\sqrt{\log \|x-y\|}},$$ answering a question posed by Ahlberg and de la Riva. This estimate recovers earlier results on the fluctuations of the passage time by Newman--Piza, Pemantle--Peres, and Chatterjee. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small ball probabilities for the passage time in planar first-passage percolation Elboim, Dor Probability We study planar first-passage percolation with independent weights whose common distribution is supported in $(0,\infty)$ and is absolutely continuous with respect to Lebesgue measure. We prove that the passage time from $x$ to $y$ denoted by $T(x,y)$ satisfies $$\max _{a\ge 0} \mathbb P \big( T(x,y)\in [a,a+1] \big) \le \frac{C}{\sqrt{\log \|x-y\|}},$$ answering a question posed by Ahlberg and de la Riva. This estimate recovers earlier results on the fluctuations of the passage time by Newman--Piza, Pemantle--Peres, and Chatterjee. |
| title | Small ball probabilities for the passage time in planar first-passage percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2406.10971 |