Related papers: Eigenvectors for a random walk on a hyperplane arr…
In [1], the authors consider a random walk $(Z_{n,1},\ldots,Z_{n,K+1})\in \mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at distance one from the following one. A functional central limit theorem for the first…
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…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We treat the right eigenvalue problem of quaternionic matrices to analysis the spectra of its transition matrix.…
This paper establishes connection between discrete cosine transform (DCT) and 1st and 2nd order discrete-time fractional Brownian motion process. It is proved that the eigenvectors of the auto-covariance matrix of a 1st and 2nd order…
The distribution of the hypervolume $V$ and surface $\partial V$ of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than $P = 10^{-1000}$ to estimate…
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…
Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display…
We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…
In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…
We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure…
In this paper, we prove a universality result of convergence for a bivariate random process defined by the eigenvectors of a sample covariance matrix. Let $V_n=(v_{ij})_{i \leq n,\, j\leq m}$ be a $n\times m$ random matrix, where $(n/m)\to…
Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's…
We study random walks on the three-strand braid group $B_3$, and in particular compute the drift, or average topological complexity of a random braid, as well as the probability of trivial entanglement. These results involve the study of…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
Staggered quantum walks on graphs are based on the concept of graph tessellation and generalize some well-known discrete-time quantum walk models. In this work, we address the class of 2-tessellable quantum walks with the goal of obtaining…
This is a first paper by the authors dedicated to the distribution of eigenvalues for random perturbations of large bidiagonal Toeplitz matrices.
We investigate the evolution of a given eigenvector of a symmetric (deterministic or random) matrix under the addition of a matrix in the Gaussian orthogonal ensemble. We quantify the overlap between this single vector with the eigenvectors…
In this paper we study random walks on the hypergroup of circles in a finite field of prime order p = 4l + 3. We investigating the behavior of random walks on this hypergroup, the equilibrium distribution and the mixing times. We use two…