Free energy of spherical Coulomb gases with point charges
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910782144380928 |
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| author | Byun, Sung-Soo Kang, Nam-Gyu Seo, Seong-Mi Yang, Meng |
| author_facet | Byun, Sung-Soo Kang, Nam-Gyu Seo, Seong-Mi Yang, Meng |
| contents | We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the north and south poles, and with microscopic point charges inserted at the poles. These models can be interpreted as Coulomb gases on the complex plane with weakly confining potentials, where the associated droplet is the entire complex plane. For these models, we derive precise asymptotic expansions of the free energies, including the constant terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free energy of spherical Coulomb gases with point charges Byun, Sung-Soo Kang, Nam-Gyu Seo, Seong-Mi Yang, Meng Mathematical Physics Complex Variables Probability We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the north and south poles, and with microscopic point charges inserted at the poles. These models can be interpreted as Coulomb gases on the complex plane with weakly confining potentials, where the associated droplet is the entire complex plane. For these models, we derive precise asymptotic expansions of the free energies, including the constant terms. |
| title | Free energy of spherical Coulomb gases with point charges |
| topic | Mathematical Physics Complex Variables Probability |
| url | https://arxiv.org/abs/2501.07284 |