Related papers: Parametric level statistics in random matrix theor…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings…
We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and…
Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime…
In this paper we extend the orthogonal polynomials approach for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar [1102.0738], to normal random matrices and 2D Coulomb gases in general. Firstly, we…
The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi-Hubbard model with dimerized hopping amplitude and find…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…
The 2d one component gas of pointlike charges in a uniform neutralizing background interacting with a logarithmic potential is a common model for plasmas. In its classical equilibrium statistics at fixed temperature (canonical ensemble) it…
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…
A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.
The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…
We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green's functions. The form of the parametric level correlation function is the…
Let $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})$ be the probability that a $N\times N$ $\beta$-ensemble of random matrices with confining potential $V(x)$ has $N_{\cal I}$ eigenvalues inside an interval ${\cal I}=[a,b]$ of the real line. We…
We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends…