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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.24529 |
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| _version_ | 1866915535502966784 |
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| author | Allard, Matthias Lahiry, Sampad |
| author_facet | Allard, Matthias Lahiry, Sampad |
| contents | We investigate a family of radially symmetric Coulomb gas systems at inverse temperature $β= 2$. The family is characterised by the property that the density of the equilibrium measure vanishes on a ring at radius $r_*$, which lies strictly inside the droplet. The large $n$ expansion of the logarithm of the partition function is obtained up to a novel $n^{1/4}$ term. We perform a double scaling limit of the correlation kernel at the $n^{1/4}$ scale and obtain a new limiting kernel in the bulk, which differs from the well-known Ginibre kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Birth of a gap: Critical phenomena in 2D Coulomb gas Allard, Matthias Lahiry, Sampad Probability Statistical Mechanics Mathematical Physics 60B20, 82D05, 41A60, 60G55 We investigate a family of radially symmetric Coulomb gas systems at inverse temperature $β= 2$. The family is characterised by the property that the density of the equilibrium measure vanishes on a ring at radius $r_*$, which lies strictly inside the droplet. The large $n$ expansion of the logarithm of the partition function is obtained up to a novel $n^{1/4}$ term. We perform a double scaling limit of the correlation kernel at the $n^{1/4}$ scale and obtain a new limiting kernel in the bulk, which differs from the well-known Ginibre kernel. |
| title | Birth of a gap: Critical phenomena in 2D Coulomb gas |
| topic | Probability Statistical Mechanics Mathematical Physics 60B20, 82D05, 41A60, 60G55 |
| url | https://arxiv.org/abs/2509.24529 |