Related papers: Random walk on hyperbolic groups and proper powers

We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…

We study the spectral theory of a reversible Markov chain associated to a hypoelliptic random walk on a manifold M. This random walk depends on a parameter h which is roughly the size of each step of the walk. We prove uniform bounds with…

Expected ballisticity of a continuous self avoiding walk on hyperbolic spaces $\mathbb{H}^d$ is established.

Strong ratio limit theorems associated with a broad class of spread out random walks on unimodular groups were proved in the preceding paper, where these random walks were assumed to have the convergence parameter $R=1$. In the present…

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum…

We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…

Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…

A simple symmetric random walk in the space $\mathbb{Z}^2$ is considered. The asymptotic behavior as the number of jumps tends to infinity of the probability that a fixed edge of the random walk lies in the polygon that forms the boundary…

Let G be an acylindrically hyperbolic group. We consider a random subgroup H in G, generated by a finite collection of independent random walks. We show that, with asymptotic probability one, such a random subgroup H of G is a free group,…

We prove the power law decay $p(t,x) \sim t^{-\phi(x,b)/2}$ in which $p(t,x)$ is the probability that the fraction of time up to $t$ in which a random walk $S$ of i.i.d. zero-mean increments taking finitely many values, is non-negative,…

Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

A probabilistic approach is provided to establish new hypergeometric identities. It is based on the calculation of moments of the limiting distribution of the position of the elephant random walk in the superdiffusive regime.

The jump processes W(t) on [0,\infty[ with transitions w -> alpha w at rate b*w^beta (0 =< alpha =< 1, b>0, beta>0) are considered. Their moments are shown to decay not faster than algebraically for t -> \infty, and an equilibrium…

We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…

We study continuous time quantum random walk on a comb with infinite teeth and show that the return probability to the starting point decays with time $t$ as $t^{-1}$. We analyse the diffusion along the spine and into the teeth and show…

We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is…

We study a large class of amenable locally compact groups containing all solvable algebraic groups over a local field and their discrete subgroups. We show that the isoperimetric profile of these groups is in some sense optimal among…