Cover time for branching random walks on regular trees

Anisotropic Branching Random Walks on Homogeneous Trees

Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundary of the tree. The random subset 3 of the boundary consisti...

Search Trees and Branching Random Walks

Branching random walks and contact processes on Galton-Watson trees

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 a Galton-Watson tree then, in certain circumstances, the branching random walks and contact processes will have weak survival phases. We also provide bounds...

A Generalized Cover Time for Random Walks on Graphs

Abstract. Given a random walk on a graph, the cover time is the rst time (number of steps) that every vertex has been hit (covered) by the walk. De ne the marking time for the walk as follows. When the walk reaches vertex vi, a coin is ipped and with probability pi the vertex is marked (or colored). We study the time that every vertex is marked. (When all the pi's are equal to 1, this gives the...

Cover time for random walks on arbitrary complex networks

We present an analytical method for computing the mean cover time of a discrete-time random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This quantity is particularly important for random search processes and target localization on network structures. Based on the global mean first-p...