Large Deviation Principles for Hypersingular Riesz Gases

Douglas P. Hardin, Thomas Leblé, Edward B. Saff, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We study N-particle systems in (Formula presented.) whose interactions are governed by a hypersingular Riesz potential (Formula presented.), (Formula presented.), and subject to an external field. We provide both macroscopic results as well as microscopic results in the limit as (Formula presented.) for random point configurations with respect to the associated Gibbs measure at scaled inverse temperature (Formula presented.). We show that a large deviation principle holds with a rate function of the form ‘(Formula presented.)-Energy + Entropy’, yielding that the microscopic behavior (on the scale (Formula presented.)) of such N-point systems is asymptotically determined by the minimizers of this rate function. In contrast to the asymptotic behavior in the integrable case (Formula presented.), where on the macroscopic scale N-point empirical measures have limiting density independent of (Formula presented.), the limiting density for (Formula presented.) is strongly (Formula presented.)-dependent.

Original languageEnglish (US)
Pages (from-to)1-40
Number of pages40
JournalConstructive Approximation
DOIs
StateAccepted/In press - May 17 2018

Fingerprint

Large Deviation Principle
Gases
Entropy
Rate Function
Temperature
Gas
Limiting
Riesz Potential
Empirical Measures
Gibbs Measure
Particle System
Minimizer
External Field

Keywords

  • Empirical measures
  • Gibbs measure
  • Large deviation principle
  • Minimal energy
  • Riesz gases

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

Cite this

Hardin, D. P., Leblé, T., Saff, E. B., & Serfaty, S. (Accepted/In press). Large Deviation Principles for Hypersingular Riesz Gases. Constructive Approximation, 1-40. https://doi.org/10.1007/s00365-018-9431-9

Large Deviation Principles for Hypersingular Riesz Gases. / Hardin, Douglas P.; Leblé, Thomas; Saff, Edward B.; Serfaty, Sylvia.

In: Constructive Approximation, 17.05.2018, p. 1-40.

Research output: Contribution to journalArticle

Hardin, Douglas P. ; Leblé, Thomas ; Saff, Edward B. ; Serfaty, Sylvia. / Large Deviation Principles for Hypersingular Riesz Gases. In: Constructive Approximation. 2018 ; pp. 1-40.
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