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Electrostatic computations for statistical mechanics and random matrix applications
Sung-Soo Byun, Peter J. Forrester
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, cho…
A Note on Optimal Soft Edge Expansions for the Gaussian Ensembles
Peter J. Forrester, Anas A. Rahman, Bo-Jian Shen
We present some review material relating to the topic of optimal asymptotic expansions of correlation functions and associated observables for ensembles in random matrix theory…
Asymptotics of the real eigenvalue distribution for the real spherical ensemble
Peter J. Forrester
The real Ginibre spherical ensemble consists of random matrices of the form , where are independent standard real Gaussian matrices. The expected numbe…
Partition function of 2D Coulomb gases with radially symmetric potentials and a hard wall
Matthias Allard, Peter J. Forrester, Sampad Lahiry +1
The large asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensiona…
On the superintegrability of the Gaussian ensemble and its generalisation
Sung-Soo Byun, Peter J. Forrester
In the present context, superintegrability is a property of certain probability density functions coming from matrix models, which relates to the average over a distinguished basis…
Finite size corrections in the bulk for circular ensembles
Peter J. Forrester, Bo-Jian Shen
The circular ensemble for and 4 corresponds to circular orthogonal, unitary and symplectic ensemble respectively as introduced by Dyson. The statistical state of the ei…
Orthogonal polynomials in the spherical ensemble with two insertions
Sung-Soo Byun, Peter J. Forrester, Arno B. J. Kuijlaars +1
We consider asymptotics of planar orthogonal polynomials (where ) with respect to the weight $$\frac{|z-w|^{2NQ_1}}{(1+|z|^2)^{N(1+Q_0+Q_1)+1}}, \q…
Properties of the one-component Coulomb gas on a sphere with two macroscopic external charges
Sung-Soo Byun, Peter J. Forrester, Sampad Lahiry
The one-component Coulomb gas on the sphere, consisting on unit charges interacting via a logarithmic potential, and in the presence of two external charges each of strength pr…