Limit theorems for vertex-reinforced jump processes on regular trees

Abstract

Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b\ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the root. Notice that it is still unknown if vertex-reinforced jump process is transient on the binary tree.

26 pages. Accepted for publication in Electronic Journal of Probability

References in corpus (5)

• A survey of random processes with reinforcement
• Recent advances in invariance principles for stationary sequences
• Vertex-reinforced random walk on Z eventually gets stuck on five points
• Recurrence of edge-reinforced random walk on a two-dimensional graph
• Attracting edge and strongly edge reinforced walks