Related papers: Joint probability densities of level spacing ratio…
Let $X$ be an $N$-dimensional random vector which describes the ordered eigenvalues of a $\beta$-Hermite ensemble, and let $z$ the vector containing the ordered zeros of the Hermite poynomial $H_N$. We present an explicit estimate for…
We derive a formula for the level spacing probability distribution in quantum graphs. We apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases. Moreover, we derive an…
In this thesis, we study three physically relevant models of strongly correlated random variables: trapped fermions, random matrices and random walks. In the first part, we show several exact mappings between the ground state of a trapped…
Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a…
We prove that in dimension one the non-real eigenvalues of the non-Hermitian Anderson (NHA) model with a selfaveraging potential are regularly spaced. The class of selfaveraging potentials which we introduce in this paper is very wide and…
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a…
In this paper, we present a general framework to solve a fundamental problem in Random Matrix Theory (RMT), i.e., the problem of describing the joint distribution of eigenvalues of the sum $\bsA+\bsB$ of two independent random Hermitian…
The theory of random matrices with eigenvalues distributed in the complex plane and more general "beta-ensembles" (logarithmic gases in 2D) is reviewed. The distribution and correlations of the eigenvalues are investigated in the large N…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real…
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
In the present work the problem of coupled disordered quantum wells is addressed in a random matrix theory framework. The quantum wells are short repulsive binary alloys embeded by ordered barriers and show well defined quantized levels as…
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…