We provide a self-contained introduction to random matrices. While some applications are
mentioned, our main emphasis is on three different approaches to random matrix models …

The semiclassical (zero‐dispersion) limit of solutions q=q(x,t,ϵ) to the one‐dimensional
focusing nonlinear Schrödinger equation (NLS) is studied in a scaling neighborhood D of a …

We consider a planar Coulomb gas ensemble of size $ N $ with the inverse temperature
$\beta= 2$ and external potential $ Q (z)=| z|^ 2-2c\log| za| $, where $ c> 0$ and …

We study large $ n $ expansions for the partition function of a Coulomb gas $$ Z_n=\frac 1
{\pi^ n}\int_ {\mathbb {C}^ n}\prod_ {1\le i< j\le n}| z_i-z_j|^ 2\prod_ {i= 1}^ ne^{-nQ (z_i)}\, d …

We study unitary random matrix ensembles of the form Z_n,N^-1|\detM|^2αe^-NTrV(M)dM,
where α>-1/2 and V is such that the limiting mean eigenvalue density for n, N→∞ and n/N→ …

We consider determinantal Coulomb gas ensembles with a class of discrete rotational
symmetric potentials whose droplets consist of several disconnected components. Under the …

We study the normal matrix model, also known as the two-dimensional one-component
plasma at a specific temperature, with merging singularity. As the number $ n $ of particles …

We consider the orthogonal polynomials with respect to the measure over the whole
complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the …

We obtain large $ N $ asymptotics for $ N\times N $ Hankel determinants corresponding to
non-negative symbols with Fisher-Hartwig (FH) singularities in the multi-cut regime. Our …

Rational solutions of the inhomogeneous Painlevé-II equation and of a related coupled
Painlevé-II system have recently arisen in studies of fluid vortices and of the sine-Gordon …