Related papers: Hypergeometric Multiple Orthogonal Polynomials and…

For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit chain, obtained by sampling…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H}_{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the…

We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above…

A measure on a locally compact group is called spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a detailed analysis of random walks on homogeneous spaces with…

We show that simple random walks on (non-trivial) relatively hyperbolic groups stay $O(\log(n))$-close to geodesics, where $n$ is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class…

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…

We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…

We consider discrete-time birth-death chains on a spider, i.e. a graph consisting of $N$ discrete half lines on the plane that are joined at the origin. This process can be identified with a discrete-time quasi-birth-death process on the…

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to…

A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…

We study a family of correlated one-dimensional random walks with a finite memory range M.These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability…

* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…

This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios involving the generalized hypergeometric function ${}_3F_2$…

We study Jacobi matrices with $N$-periodically modulated recurrence coefficients when the sequence of $N$-step transfer matrices is convergent to a non-trivial Jordan block. In particular, we describe asymptotic behavior of their…

We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…

General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied through both right and left multiplication to a rectangular…

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments…

In this paper, we study the stochastic homogenization for a class of symmetric random walks in random conductance model, whose one-step transition probability from $x$ to $y$ is proportional to $|x-y|^{-d-2}$. As the associated jumping…

This paper is motivated by the following problem. Define a quantum walk on a positively weighted path (linear chain). Can the weights be tuned so that perfect state transfer occurs between the first vertex and any other position? We do not…