Limit theorems for vertex-reinforced jump processes on regular trees. (English) Zbl 1189.60170

Summary: Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly b children, with b \(\geq 3\). 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.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F15 Strong limit theorems
60F05 Central limit and other weak theorems
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