Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913147304017920 |
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| author | Feldheim, Naomi Feldheim, Ohad Muirhead, Stephen |
| author_facet | Feldheim, Naomi Feldheim, Ohad Muirhead, Stephen |
| contents | We compute the exact log-asymptotics of the persistence probability, and determine the entropic repulsion profile conditioned on persistence, for general $d$-dimensional stationary Gaussian fields with spectral singularity at the origin of order $α\in [0,d)$. Under mild regularity conditions these are shown to be universal, depending only on $α$ and $d$, and to have explicit formulations in terms of the capacity and equilibrium potential of the $α$-Riesz kernel. This generalises a result of Bolthausen, Deuschel and Zeitouni on the Gaussian free field to a wide class of Gaussian fields with spectral singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20587 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin Feldheim, Naomi Feldheim, Ohad Muirhead, Stephen Probability We compute the exact log-asymptotics of the persistence probability, and determine the entropic repulsion profile conditioned on persistence, for general $d$-dimensional stationary Gaussian fields with spectral singularity at the origin of order $α\in [0,d)$. Under mild regularity conditions these are shown to be universal, depending only on $α$ and $d$, and to have explicit formulations in terms of the capacity and equilibrium potential of the $α$-Riesz kernel. This generalises a result of Bolthausen, Deuschel and Zeitouni on the Gaussian free field to a wide class of Gaussian fields with spectral singularity. |
| title | Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin |
| topic | Probability |
| url | https://arxiv.org/abs/2605.20587 |