Extremal process of the zero-average Gaussian Free Field for $d\ge 3$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917678477737984 |
|---|---|
| author | Das, Sayan Hazra, Rajat Subhra |
| author_facet | Das, Sayan Hazra, Rajat Subhra |
| contents | We consider the Gaussian free field on the torus whose covariance kernel is given by the zero-average Green's function. We show that for dimension $d\ge 3$, the extremal point process associated with this field converges weakly to a Poisson random measure. As an immediate corollary, the maxima of the field converges after appropriate centering and scaling to the Gumbel distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_03500 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Extremal process of the zero-average Gaussian Free Field for $d\ge 3$ Das, Sayan Hazra, Rajat Subhra Probability We consider the Gaussian free field on the torus whose covariance kernel is given by the zero-average Green's function. We show that for dimension $d\ge 3$, the extremal point process associated with this field converges weakly to a Poisson random measure. As an immediate corollary, the maxima of the field converges after appropriate centering and scaling to the Gumbel distribution. |
| title | Extremal process of the zero-average Gaussian Free Field for $d\ge 3$ |
| topic | Probability |
| url | https://arxiv.org/abs/1808.03500 |