Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius

Details Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius

2007-10-30

arxiv.org/abs/0710.5745v4

Mathematics

Probability

Minor corrections of version 2

Scientific paper

It is proved that the Green's function of the simple random walk on a surface group of large genus decays exponentially at the spectral radius. It is also shown that Ancona's inequalities extend to the spectral radius R, and therefore that the Martin boundary for R-potentials coincides with the natural geometric boundary S^1. This implies that the Green's function obeys a power law with exponent 1/2 at the spectral radius.

Affiliated with

Also associated with

No associations

Rating

Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius 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 Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Walk on a Surface Group: Boundary Behavior of the Green's Function at the Spectral Radius will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-366107