## Electronic Communications in Probability

### Asymptotic results in solvable two-charge models

#### 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
Accepted: 5 February 2018
First available in Project Euclid: 27 February 2018

https://projecteuclid.org/euclid.ecp/1519722246

Digital Object Identifier
doi:10.1214/18-ECP115

Mathematical Reviews number (MathSciNet)
MR3771774

Zentralblatt MATH identifier
1388.60023

#### 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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