Related papers: Universal Behavior of Correlations between Eigenva…
Statistical properties of non--symmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices are investigated. We derive an exact formula for the density of eigenvalues which consists of two…
When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the…
Mutualistic networks are used to study the structure and processes inherent to mutualistic relationships. In this paper, we introduce a random matrix ensemble (RME) representing the adjacency matrices of mutualistic networks composed by two…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dirac spectra and discuss the relation between chiral symmetry…
This short note studies the fluctuations of the largest eigenvalue of symmetric random matrices with correlated Gaussian entries having positive mean. Under the assumption that the covariance kernel is absolutely summable, it is proved that…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over 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…
We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences…
We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…