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2018 Asymptotic results in solvable two-charge models
Martina Dal Borgo, Emma Hovhannisyan, Alain Rouault
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP115


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.


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Martina Dal Borgo. Emma Hovhannisyan. Alain Rouault. "Asymptotic results in solvable two-charge models." Electron. Commun. Probab. 23 1 - 12, 2018.


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

zbMATH: 1388.60023
MathSciNet: MR3771774
Digital Object Identifier: 10.1214/18-ECP115

Primary: 15A15, 15B52, 60B20, 82B05
Secondary: 33C45, 60F05, 60F10, 60G55, 62H10


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