Free energy and fluctuations in the random normal matrix model with spectral gaps

2023/12/21 by Yacin Ameur, Ameur, Yacin, Christophe Charlier +3 · 6 citations
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.13904

openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study large n expansions for the partition function of a Coulomb gas Z_n=\frac 1 πⁿ∫_ℂⁿ∏_1≤ i

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• Free-energy variations for determinantal 2D plasmas with holes
• Partition functions of two-dimensional Coulomb gases with circular root- and jump-type singularities
• Birth of a gap: Critical phenomena in 2D Coulomb gas

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