A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

Fabio Deelan Cunden; Paolo Facchi; Pierpaolo Vivo

doi:10.1088/1751-8113/49/13/135202

A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

Fabio Deelan Cunden, Paolo Facchi, Pierpaolo Vivo

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Abstract

In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues

Original language	English
Article number	135202
Number of pages	19
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	49
Issue number	13
Early online date	17 Feb 2016
DOIs	https://doi.org/10.1088/1751-8113/49/13/135202
Publication status	Published - 1 Apr 2016

Keywords

random matrix theory
2D Coulomb gas
large deviations
phase transitions

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Wegner estimates and universality for non-Hermitian matrices
Mezzadri, F. (Principal Investigator)
1/05/14 → 31/10/17
Project: Research

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AB - In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues

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KW - 2D Coulomb gas

KW - large deviations

KW - phase transitions

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DO - 10.1088/1751-8113/49/13/135202

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A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

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Wegner estimates and universality for non-Hermitian matrices

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