Random walks on trees and the law of iterated logarithm
Kolmogorov's law of iterated logarithm is used to provide conditions [see also \textit{M. Konsowa} and \textit{J. Mitro}, J. Theor. Probab. 4, No. 3, 535-550 (1991; Zbl 0725.60073)] for the recurrence or transience of a simple random walk on (infinite) \(\mathbb N\)-trees in which all vertices with the same distance from the root have the same degree.
scientific article; zbMATH DE number 1796678