Limit theorems for vertex-reinforced jump processes on regular trees

Details Limit theorems for vertex-reinforced jump processes on regular trees Limit theorems for vertex-reinforced jump processes on regular trees

2009-07-28

arxiv.org/abs/0907.4854v1

Mathematics

Probability

26 pages. Accepted for publication in Electronic Journal of Probability

Scientific paper

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.

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