Large deviation principle for empirical fields of Log and Riesz gases

Thomas Leblé, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which arise in random matrix theory. We also give a next-to-leading order expansion of the free energy of the system, proving the existence of the thermodynamic limit.

Original languageEnglish (US)
Pages (from-to)1-113
Number of pages113
JournalInventiones Mathematicae
DOIs
StateAccepted/In press - Jun 7 2017

Fingerprint

Large Deviation Principle
Random Matrix Theory
Rate Function
Relative Entropy
Thermodynamic Limit
Term
Energy
Free Energy
Pairwise
Deduce
Logarithmic
Entropy
Interaction
Gas

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Large deviation principle for empirical fields of Log and Riesz gases. / Leblé, Thomas; Serfaty, Sylvia.

In: Inventiones Mathematicae, 07.06.2017, p. 1-113.

Research output: Contribution to journalArticle

@article{2ade20216ac04d4ea8e5760cba644bce,
title = "Large deviation principle for empirical fields of Log and Riesz gases",
abstract = "We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which arise in random matrix theory. We also give a next-to-leading order expansion of the free energy of the system, proving the existence of the thermodynamic limit.",
author = "Thomas Lebl{\'e} and Sylvia Serfaty",
year = "2017",
month = "6",
day = "7",
doi = "10.1007/s00222-017-0738-0",
language = "English (US)",
pages = "1--113",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",

}

TY - JOUR

T1 - Large deviation principle for empirical fields of Log and Riesz gases

AU - Leblé, Thomas

AU - Serfaty, Sylvia

PY - 2017/6/7

Y1 - 2017/6/7

N2 - We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which arise in random matrix theory. We also give a next-to-leading order expansion of the free energy of the system, proving the existence of the thermodynamic limit.

AB - We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which arise in random matrix theory. We also give a next-to-leading order expansion of the free energy of the system, proving the existence of the thermodynamic limit.

UR - http://www.scopus.com/inward/record.url?scp=85020265417&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020265417&partnerID=8YFLogxK

U2 - 10.1007/s00222-017-0738-0

DO - 10.1007/s00222-017-0738-0

M3 - Article

SP - 1

EP - 113

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

ER -