Volume growth and heat kernel estimates for the continuum random tree

Details Volume growth and heat kernel estimates for the continuum random tree Volume growth and heat kernel estimates for the continuum random tree

2006-12-20

arxiv.org/abs/math/0612585v2

Mathematics

Probability

Scientific paper

In this article, we prove global and local (point-wise) volume and heat kernel bounds for the continuum random tree. We demonstrate that there are almost-surely logarithmic global fluctuations and log-logarithmic local fluctuations in the volume of balls of radius $r$ about the leading order polynomial term as $r\to0$. We also show that the on-diagonal part of the heat kernel exhibits corresponding global and local fluctuations as $t\to0$ almost-surely. Finally, we prove that this quenched (almost-sure) behaviour contrasts with the local annealed (averaged over all realisations of the tree) volume and heat kernel behaviour, which is smooth.

Affiliated with

Also associated with

No associations

Rating

Volume growth and heat kernel estimates for the continuum random tree 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 Volume growth and heat kernel estimates for the continuum random tree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Volume growth and heat kernel estimates for the continuum random tree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-242526