Fluctuations around the diagonal in Bernoulli-Exponential first passage percolation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917768667856896 |
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| author | Vető, Bálint |
| author_facet | Vető, Bálint |
| contents | We prove that the rescaled one-point fluctuations of the boundary of the percolation cluster in the Bernoulli-Exponential first passage percolation around the diagonal converge to a new family of distributions. The limit law is indexed by the rescaled level of percolation $s\ge0$, it is Gaussian for $s=0$ and it converges to the Tracy--Widom distribution as $s\to\infty$. For a fixed level $s>0$ the width of the cluster in the limit as a function of a time parameter $t$ is of order $t^{2/3}$ with Tracy--Widom fluctuations as in the discrete model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fluctuations around the diagonal in Bernoulli-Exponential first passage percolation Vető, Bálint Probability We prove that the rescaled one-point fluctuations of the boundary of the percolation cluster in the Bernoulli-Exponential first passage percolation around the diagonal converge to a new family of distributions. The limit law is indexed by the rescaled level of percolation $s\ge0$, it is Gaussian for $s=0$ and it converges to the Tracy--Widom distribution as $s\to\infty$. For a fixed level $s>0$ the width of the cluster in the limit as a function of a time parameter $t$ is of order $t^{2/3}$ with Tracy--Widom fluctuations as in the discrete model. |
| title | Fluctuations around the diagonal in Bernoulli-Exponential first passage percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2306.09073 |