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Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
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…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
This paper is concerned with complex eigenvalues of truncated unitary quaternion matrices equipped with the Haar measure. The joint eigenvalue probability density function is obtained for truncations of any size. We also obtain the spectral…
A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre…
Inhomogeneous random matrices with non-trivial variance profiles determined by symmetric stochastic matrices and with independent sub-Gaussian entries up to Hermitian symmetry, encompass a wide range of important models, including sparse…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…