相关论文: Cutpoints and resistance of random walk paths

The Transience objective is not to visit any state infinitely often. While this is not possible in finite Markov Decision Process (MDP), it can be satisfied in countably infinite ones, e.g., if the transition graph is acyclic. We prove the…

In this article we consider transient random walks on free products of graphs. We prove that the asymptotic range of these random walks exists and is strictly positive. In particular, we show that the range varies real-analytically in terms…

We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…

A coupling of random walkers on the same finite graph, who take turns sequentially, is said to be an avoidance coupling if the walkers never collide. Previous studies of these processes have focused almost exclusively on complete graphs, in…

A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…

Let G be a vertex transitive graph. A study of the range of simple random walk on G and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its…

Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…

In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…

A (directed) temporal graph is a (directed) graph whose edges are available only at specific times during its (discretized) lifetime $\tau$. In this setting, we ask that walks respect the temporal aspect by defining $\textit{temporal…

In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…

Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is…

The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…

We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…

The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…

We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of…

We examine the mixing time for random walks on graphs. In particular we are interested on investigating graphs with bottlenecks. Furthermore, the cutoff phenomenon is examined.

We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…

We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…

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,…

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…