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arXiv · 2412.15825

Generic regularity of equilibrium measures for the logarithmic potential with external fields

Giacomo Colombo·Alessio Figalli
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Abstract

It is a well-known conjecture in $\beta$-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.

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Giacomo Colombo, Alessio Figalli. 2024-12-20. Generic regularity of equilibrium measures for the logarithmic potential with external fields. https://doi.org/10.1007/s00220-026-05710-5

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