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arXiv · 2303.09912

Law of large numbers for the maximum of the two-dimensional Coulomb gas potential

Gaultier Lambert·Thomas Leblé·Ofer Zeitouni
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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.

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Gaultier Lambert, Thomas Leblé, Ofer Zeitouni. 2023-03-17. Law of large numbers for the maximum of the two-dimensional Coulomb gas potential. https://arxiv.org/abs/2303.09912

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