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

Authors

  • Klara Courteaut KTH Royal Institute of Technology, Department of Mathematics
  • Kurt Johansson KTH Royal Institute of Technology, Department of Mathematics

DOI:

https://doi.org/10.54330/afm.159822

Keywords:

Log-gas, Coulomb gas, Jordan curve, partition function, free energy, Central Limit Theorem, global fluctuations, linear statistic

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. 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.

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Published

2025-03-13

Issue

Vol. 50 No. 1 (2025)

Section

Articles

License

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Courteaut, K., & Johansson, K. (2025). Partition function for the 2d Coulomb gas on a Jordan curve. Annales Fennici Mathematici, 50(1), 109–144. https://doi.org/10.54330/afm.159822