Related papers: Random sparse generators of Markovian evolution an…

We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…

We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graph ${\bf G}(N,p)$. For $N^{-1+o(1)}\leq p\leq 1/2$, we show that the non-trivial edge eigenvectors are asymptotically jointly normal.…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…

The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming non-zero at the transition. It has been proposed previously that the vibrational…

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…

To a unitary matrix U we associate a doubly stochastic matrix M by taking the modulus squared of each element of U. To study the connection between onset of quantum chaos on graphs and ergodicity of the underlying Markov chain, specified by…

We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd{\H o}s-R{\'e}nyi graph $G(N,p)$. Recently, it was shown by Lee, up to an…

In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are…

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…

Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…

We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…

We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…

We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization…

Sparse superposition codes were originally proposed as a capacity-achieving communication scheme over the gaussian channel, whose coding matrices were made of i.i.d. gaussian entries.We extend this coding scheme to more generic ensembles of…

It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…