Related papers: Random walk on surfaces with hyperbolic cusps

Consider a symmetric aperiodic random walk in $Z^d$, $d\geq 3$. There are points (called heavy points) where the number of visits by the random walk is close to its maximum. We investigate the local times around these heavy points and show…

We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven…

We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular we prove that if a convergence group $G$ acts on a compact metrizable space $M$ with the convergence property then we can…

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…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…

We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.

Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…

In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if…

In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4,…

The aim of this work is to study the convergence to equilibrium of an $(h,\rho)$-subelliptic random walk on a closed, connected Riemannian manifold $(M,g)$ associated with a subelliptic second-order differential operator $A$ on $M$. In such…

Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound from below for this spectral…

Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…

We consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube, and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the…

We study Lam's reduced random walk in a hyperbolic triangle group, which we view as a random walk in the upper half-plane. We prove that this walk converges almost surely to a point on the extended real line. We devote special attention to…

We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

We analyze a model of hypercubic random surfaces with an extrinsic curvature term in the action. We find a first order phase transition at finite coupling separating a branched polymer from a stable flat phase.

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…

We study a class of symmetric quantum walks on Hamming graphs, where the distance between vertices specifies the transition probability. A special model is the simple quantum walk on the hypercube, which has been discussed in the…

Let $G$ be a connected simple real Lie group, $\Lambda_{0}\subseteq G$ a lattice and $\Lambda \unlhd \Lambda_{0}$ a normal subgroup such that $\Lambda_{0}/\Lambda\simeq \mathbb{Z}^d$. We study the drift of a random walk on the…