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

Collevecchio, Andrea

Electron. J. Probab. 14, 1936-1962 (2009).

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

Keywords:

reinforced random walks; strong law of large numbers; central limit theorem