Abstract
We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of exponential moments, and the theory of Gaussian multiplicative chaos.
Funding Statement
G.L. acknowledges the supports of the Ambizione grant S-71114-05-01 from the Swiss National Science Foundation and of the starting grant 2022-04882 from the Swedish Research Council. T.L. acknowledges the support of JCJC grant ANR-21-CE40-0009 from Agence Nationale de la Recherche. The third author was partially supported by Israel Science Foundation grant number 421/20.
Acknowledgments
We thank Sylvia Serfaty for communicating early versions of [Ser23] to us and making some statements thereof more easily citable for our purposes. We thank the anonymous referees for comments that improved the presentation of our results, and for a careful reading.
Citation
Gaultier Lambert. Thomas Leblé. Ofer Zeitouni. "Law of large numbers for the maximum of the two-dimensional Coulomb gas potential." Electron. J. Probab. 29 1 - 36, 2024. https://doi.org/10.1214/24-EJP1102
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