Related papers: Universal correlators for multi-arc complex matrix…

We derive the large-N spectral correlators of complex matrix ensembles with weights that in the context of Dirac spectra correspond to N_f massive fermions, and prove that the results are universal in the appropriate scaling limits. The…

Properties of universality have essential relevance for the theory of random matrices usually called the Wigner ensemble. The issue was analysed up to recent years with detailed and relevant results. We present a slightly different view and…

Universality in unitary invariant random matrix ensembles with complex matrix elements is considered. We treat two general ensembles which have a determinant factor in the weight. These ensembles are relevant, e.g., for spectra of the Dirac…

In this paper the kernel for the spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the…

We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws…

We rewrite the loop equations of the hermitian matrix model, in a way which allows to compute all the correlation functions, to all orders in the topological $1/N^2$ expansion, as residues on an hyperelliptical curve. Those residues, can be…

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…

For a given polynomial $V(x)\in \mathbb C[x]$, a random matrix eigenvalues measure is a measure $\prod_{1\leq i<j\leq N}(x_i-x_j)^2 \prod_{i=1}^N e^{-V(x_i)}dx_i$ on $\gamma^N$. Hermitian matrices have real eigenvalues $\gamma=\mathbb R$,…

The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…

We consider complex, weakly non-Hermitian matrices $A = W_1 +i\sqrt{{\tau}_N}W_2$ , where $W_1$ and $W_2$ are Hermitian matrices and $\tau_N = O(N^{-1})$. We first show that for pairs of Hermitian matrices $(W_1 , W_2)$ such that $W_1$…

We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the determinant formulas for correlation functions in…

We consider a Hamiltonian $ H = H_0+ V $, in which $ H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of…

We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We…

We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…

We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft…

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The…

We consider unitary random matrix ensembles Z_{n,s,t}^{-1}e^{-n tr V_{s,t}(M)}dM on the space of Hermitian n x n matrices M, where the confining potential V_{s,t} is such that the limiting mean density of eigenvalues (as n\to\infty and…

Using large $N$ arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large $N$ limit. The setting generalizes the quaternionic extension of free probability to…