Law of Large Numbers for the Maximum of the Two-Dimensional Coulomb Gas Potential

Gaultier Lambert,Thomas Leble,Ofer Zeitouni

Electronic Journal of Probability（2024）SCI 3区

Cited 2|Views7

Abstract

We derive the leading order asymptotics of the logarithmic potential of a twodimensional Coulomb gas at arbitrary positive temperature. The proof is basedon precise evaluation of exponential moments, and the theory of Gaussianmultiplicative chaos.

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Key words

Coulomb Gas,log-correlated fields,Gaussian Multiplicative Chaos

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