Random walks on trees and the law of iterated logarithm

✍ Scribed by Mokhtar H. Konsowa

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 80 KB
• Volume: 56
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00185-7

✦ Synopsis

In this paper we give an alternative proof for the main result of Konsowa and Mitro (J. Theor. Probab. 4 (3) (1991) 535), Konsowa and Mitro found that the simple random walk (SRW) on inÿnite trees is transient or recurrent. In part of their work, they considered the case of an N-tree in which all the vertices of the same distance n from the root have the same degree which is 3 with probability q n and 2 with probability 1 -q n . They proved that the SRW is transient if lim inf nq n ¿ 1=log 2 and recurrent if lim sup nq n ¡ 1=log 2. We ÿnd that the Kolmogorov's law of iterated logarithm is a natural tool to tackle this problem and use it to give an alternative proof.