Related papers: Recursive characterisations of random matrix ensem…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…

Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.

In this paper we present a new family of discrete sequences having "random like" uniformly decaying auto-correlation properties. The new class of infinite length sequences are higher order chirps constructed using irrational numbers.…

We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…

We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…

Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…

In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such…

We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…

Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…

This paper presents a novel approach to binary classification using dynamic logistic ensemble models. The proposed method addresses the challenges posed by datasets containing inherent internal clusters that lack explicit feature-based…

Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…

We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…

Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…

We initiate a systematic investigation of Mellin amplitudes of Witten diagrams to all loop levels, by introducing integral recursion relations among them. Focusing on the scalar effective theories in AdS with the simplest type of…

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…