Extremal particles of two-dimensional Coulomb gases and random polynomials on a positive background

DOI10.1214/21-AAP1682zbMath1492.60267arXiv1811.12225MaRDI QIDQ2117449

David García-Zelada, Raphaël Butez

Publication date: 21 March 2022

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12225

zbMATH Keywords

Bergman kernelGibbs measureCoulomb gasinteracting particle systemrandom polynomialdeterminantal point process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (6)

Convergence of the spectral radius of a random matrix through its characteristic polynomial ⋮ Edge fluctuations for random normal matrix ensembles ⋮ At the edge of a one-dimensional jellium ⋮ Edge behavior of two-dimensional Coulomb gases near a hard wall ⋮ Gap probability and full counting statistics in the one-dimensional one-component plasma ⋮ Macroscopic and edge behavior of a planar jellium

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on large deviations for 2D Coulomb gas with weakly confining potential
• Universal large deviations for Kac polynomials
• Spectral radii of large non-Hermitian random matrices
• A note on the second order universality at the edge of Coulomb gases on the plane
• Continuum limits of random matrices and the Brownian carousel
• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Random point fields associated with certain Fredholm determinants. I: Fermion, Poisson and Boson point processes.
• Systems of points with Coulomb interactions
• Spectral radii of truncated circular unitary matrices
• On bulk singularities in the random normal matrix model
• Limiting distributions of spectral radii for product of matrices from the spherical ensemble
• The largest root of random Kac polynomials is heavy tailed
• A localization theorem for the planar Coulomb gas in an external field
• Planar orthogonal polynomials and boundary universality in the random normal matrix model
• On boundary confinements for the Coulomb gas
• Asymptotic zero distribution of random orthogonal polynomials
• Rescaling Ward identities in the random normal matrix model
• A large deviation principle for empirical measures on Polish spaces: application to singular Gibbs measures on manifolds
• Determinantal point processes and fermions on polarized complex manifolds: bulk universality
• Rigidity for zero sets of Gaussian entire functions
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
• Über die Nullstellenverteilung zufälliger Polynome
• Edge scaling limit of the spectral radius for random normal matrix ensembles at hard edge
• On Distribution of Zeros of Random Polynomials in Complex Plane
• The Ginibre Ensemble and Gaussian Analytic Functions
• Random Measures, Theory and Applications
• Large Deviations of Empirical Measures of Zeros of Random Polynomials
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• A limit theorem at the edge of a non-Hermitian random matrix ensemble
• Extremes of 2d Coulomb gas: universal intermediate deviation regime
• Macroscopic and edge behavior of a planar jellium
• Local Universality of Zeroes of Random Polynomials

This page was built for publication: Extremal particles of two-dimensional Coulomb gases and random polynomials on a positive background