Growth Series and Random Walks on Some Hyperbolic Graphs

Details Growth Series and Random Walks on Some Hyperbolic Graphs Growth Series and Random Walks on Some Hyperbolic Graphs

2001-09-11

arxiv.org/abs/math/0109069v2

Monatsh. Math. 136 (2002), no. 3, 181--202

Mathematics

Group Theory

21 pages. to appear in monash. math

Scientific paper

10.1007/s006050200043

Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a family of reduced loops in these graphs. We then apply Grigorchuk's result relating cogrowth and random walks to obtain lower estimates on the spectral radius of the Markov operator associated with a symmetric random walk on these graphs.

Affiliated with

Also associated with

No associations

Rating

Growth Series and Random Walks on Some Hyperbolic Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Growth Series and Random Walks on Some Hyperbolic Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth Series and Random Walks on Some Hyperbolic Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-711059