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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.15825 |
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| _version_ | 1866911143372521472 |
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| author | Colombo, Giacomo Figalli, Alessio |
| author_facet | Colombo, Giacomo Figalli, Alessio |
| contents | It is a well-known conjecture in $β$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and thin obstacle problems, we give a positive answer to this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic regularity of equilibrium measures for the logarithmic potential with external fields Colombo, Giacomo Figalli, Alessio Probability Analysis of PDEs 60B20, 35R35, 35B65 It is a well-known conjecture in $β$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and thin obstacle problems, we give a positive answer to this conjecture. |
| title | Generic regularity of equilibrium measures for the logarithmic potential with external fields |
| topic | Probability Analysis of PDEs 60B20, 35R35, 35B65 |
| url | https://arxiv.org/abs/2412.15825 |