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Partition function for the 2d Coulomb gas on a Jordan curve

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arxiv 2304.09726 v3 pith:MX7V44ER submitted 2023-04-19 math.PR math.CV

Klara Courteaut , Kurt Johansson This is my paper · ORCID
classification math.PRmath.CV
keywords curveasymptoticcoulombfunctionjordanpartitionbetacentral
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abstract

We prove an asymptotic formula for the partition function of a 2d Coulomb gas at inverse temperature $\beta>0$ confined to lie on a Jordan curve. This also gives a central limit theorem for a linear statistic of the particles in the gas. We obtain different expressions for the asymptotic mean and variance which involve either the exterior conformal mapping of the curve or the Grunsky operator.

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  1. Planar Coulomb gas on a Jordan arc at any temperature

    math.CV 2025-04 accept novelty 7.0 of 10

    The free energy of the 2D Coulomb gas on a Jordan arc has asymptotic constant term (1/24)J^A(γ)+(1/8)(√(β/2)-√(2/β))^2 J^F(γ), where J^A and J^F are geometric energies of the arc and its opened Jordan curve.

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