Electronic Communications in Probability

Asymptotic results in solvable two-charge models

Martina Dal Borgo, Emma Hovhannisyan, and Alain Rouault

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Abstract

In [16], a solvable two charge ensemble of interacting charged particles on the real line in the presence of the harmonic oscillator potential is introduced. It can be seen as a special form of a grand canonical ensemble with the total charge being fixed and unit charge particles being random. Moreover, it serves as an interpolation between the Gaussian orthogonal and the Gaussian symplectic ensembles and maintains the Pfaffian structure of the eigenvalues. A similar solvable ensemble of charged particles on the unit circle was studied in [17, 10].

In this paper we explore the sharp asymptotic behavior of the number of unit charge particles on the line and on the circle, as the total charge goes to infinity. We establish extended central limit theorems, Berry-Esseen estimates and precise moderate deviations using the machinery of the mod-Gaussian convergence developed in [6, 15, 14, 4, 7]. Also a large deviation principle is derived using the Gärtner-Ellis theorem.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 16, 12 pp.

Dates
Received: 1 November 2017
Accepted: 5 February 2018
First available in Project Euclid: 27 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1519722246

Digital Object Identifier
doi:10.1214/18-ECP115

Mathematical Reviews number (MathSciNet)
MR3771774

Zentralblatt MATH identifier
1388.60023

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 82B05: Classical equilibrium statistical mechanics (general) 15B52: Random matrices 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] 60G55: Point processes 60F05: Central limit and other weak theorems 60F10: Large deviations 62H10: Distribution of statistics

Keywords
random matrices two-charge ensembles large deviation principle moderate deviations central limit theorem Berry-Esseen estimate local limit theorem Gaussian orthogonal ensemble circular orthogonal ensemble

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dal Borgo, Martina; Hovhannisyan, Emma; Rouault, Alain. Asymptotic results in solvable two-charge models. Electron. Commun. Probab. 23 (2018), paper no. 16, 12 pp. doi:10.1214/18-ECP115. https://projecteuclid.org/euclid.ecp/1519722246


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