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

2024/12/20 by Colombo, Giacomo, Figalli, Alessio
#35B65 #35R35 #60B20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2412.15825

Abstract

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.

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