Extremes of the zero-average Gaussian Free Field on random regular graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914162050859008 |
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| author | Hartung, Lisa Klippel, Andreas Mönch, Christian |
| author_facet | Hartung, Lisa Klippel, Andreas Mönch, Christian |
| contents | We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random $r$-regular graphs and the Gaussian free field on $r$-regular trees. For random $r$-regular graphs of diverging size, for every fixed $r\ge3$, we show that the rescaled extremal point process of the field is asymptotically distributed, in the annealed sense, as a Poisson point process on the line with intensity $e^{-x}\,\mathrm{d}x$. The same limit behaviour is obeyed by the restriction of the GFF on $r$-regular trees to finite subsets of vertices. Our approach relies on a direct Gaussian comparison argument and precise Green function estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremes of the zero-average Gaussian Free Field on random regular graphs Hartung, Lisa Klippel, Andreas Mönch, Christian Probability 60G70 (Primary) 60K35, 05C80 (Secondary) We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random $r$-regular graphs and the Gaussian free field on $r$-regular trees. For random $r$-regular graphs of diverging size, for every fixed $r\ge3$, we show that the rescaled extremal point process of the field is asymptotically distributed, in the annealed sense, as a Poisson point process on the line with intensity $e^{-x}\,\mathrm{d}x$. The same limit behaviour is obeyed by the restriction of the GFF on $r$-regular trees to finite subsets of vertices. Our approach relies on a direct Gaussian comparison argument and precise Green function estimates. |
| title | Extremes of the zero-average Gaussian Free Field on random regular graphs |
| topic | Probability 60G70 (Primary) 60K35, 05C80 (Secondary) |
| url | https://arxiv.org/abs/2511.14026 |