Random Walks on Trees with Finitely Many Cone Types

Content Provider	Semantic Scholar
Author	Nagnibeda, Tatiana Woess, Wolfgang
Copyright Year	2002
Abstract	This paper is devoted to the study of random walks on infinite trees with finitely many cone types (also called periodic trees). We consider nearest neighbour random walks with probabilities adapted to the cone structure of the tree, which include in particular the well studied classes of simple and homesick random walks. We give a simple criterion for transience or recurrence of the random walk and prove that the spectral radius is equal to 1 if and only if the random walk is recurrent. Furthermore, we study the asymptotic behaviour of return probabilitites and prove a local limit theorem. In the transient case, we also prove a law of large numbers and compute the rate of escape of the random walk to infinity, as well as prove a central limit theorem. Finally, we describe the structure of the boundary process and explain its connection with the random walk.
Starting Page	383
Ending Page	422
Page Count	40
File Format	PDF HTM / HTML
DOI	10.1023/A:1014810827031
Volume Number	15
Alternate Webpage(s)	http://www.cis.tugraz.at/mathc/woess/jtp.pdf
Alternate Webpage(s)	http://www.math.tugraz.at/~woess/papers/jtp.pdf
Alternate Webpage(s)	https://doi.org/10.1023/A%3A1014810827031
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article