Free-energy variations for determinantal 2D plasmas with holes

2025/10/02 by Nicolas Rougerie, Rougerie, Nicolas · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.2510.01745

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We study the Gibbs equilibrium of a classical 2D Coulomb gas in the determinantal case β = 2. The external potential is the sum of a quadratic term and the potential generated by individual charges pinned in several extended groups. This leads to an equilibrium measure (droplet) with flat density and macroscopic holes. We consider ''correlation energy'' (free energy minus its mean-field approximation) expansions, for large particle number N. Under the assumptions that the holes are sufficiently small, separated, and far from the droplet's outer boundary, we prove that (i) the correlation energy up to order 1 is independent of the holes' locations and orientations, and (ii) the difference between the correlation energies of systems differing by their number of holes essentially consists of ``topological'' O(logN) and O(1) terms.

Citations

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Cited by

• Precise large deviations in geometric last passage percolation
• Free energy of the Coulomb gas in the determinantal case on Riemann surfaces

Related

• Birth of a gap: Critical phenomena in 2D Coulomb gas
• Determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials
• The two-dimensional Coulomb gas: fluctuations through a spectral gap
• Smallest gaps of the two-dimensional Coulomb gas
• Free energy of spherical Coulomb gases with point charges