## 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.

### MSC:

 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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