Geodesic
Partition function for the 2d Coulomb gas on a Jordan curve
Klara Courteaut1 ; Kurt Johansson1
1KTH Royal Institute of Technology, Department of Mathematics
Annales Fennici Mathematici, Tome 50 (2025) no. 1, p. 109–144

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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. The partition function can include a linear statistic. The asymptotic formula involves a Fredholm determinant related to the Loewner energy of the curve, and also an expression involving the sampling function, the exterior conformal map for the curve and the Grunsky operator. The asymptotic formula also gives a central limit theorem for linear statistics of the particles in the gas.
DOI : 10.54330/afm.159822
Keywords: Log-gas, Coulomb gas, Jordan curve, partition function, free energy, Central Limit Theorem, global fluctuations, linear statistic

Klara Courteaut  1   ; Kurt Johansson  1

1 KTH Royal Institute of Technology, Department of Mathematics 
Klara Courteaut; Kurt Johansson. Partition function for the 2d Coulomb gas on a Jordan curve. Annales Fennici Mathematici, Tome 50 (2025) no. 1, p. 109–144. doi: 10.54330/afm.159822
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