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Mathematics > Probability

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

Authors: Gaultier Lambert, Thomas Leblé, Ofer Zeitouni
(Submitted on 17 Mar 2023 (v1), last revised 13 Feb 2024 (this version, v2))
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.
Comments: 33p. Added full definitions and more details about our main imports from the literature. Minor corrections
Subjects: Probability (math.PR); Mathematical Physics (math-ph)
Cite as: arXiv:2303.09912 [math.PR]
  (or arXiv:2303.09912v2 [math.PR] for this version)

Submission history

From: Thomas Leblé [view email]
[v1] Fri, 17 Mar 2023 12:03:56 GMT (34kb)
[v2] Tue, 13 Feb 2024 07:07:06 GMT (686kb)
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