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<p>A well-known conjecture in the theory of Coulomb gases and the mean-field limit of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-ensembles asserts that, generically, external potentials are “off-critical” (or equivalently, “regular”). By exploiting the connection between minimizing measures and thin obstacle problems, we establish this conjecture.</p>

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Generic Regularity of Equilibrium Measures for the Logarithmic Potential with External Fields

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Giacomo Colombo,
  • Alessio Figalli

摘要

A well-known conjecture in the theory of Coulomb gases and the mean-field limit of \(\beta \) β -ensembles asserts that, generically, external potentials are “off-critical” (or equivalently, “regular”). By exploiting the connection between minimizing measures and thin obstacle problems, we establish this conjecture.