Upper bound on the expected size of intrinsic ball
Probability
2010-06-09 v1
Abstract
We give a short proof of Theorem 1.2 (i) from the paper "The Alexander-Orbach conjecture holds in high dimensions" by G. Kozma and A. Nachmias. We show that the expected size of the intrinsic ball of radius r is at most Cr if the susceptibility exponent is at most 1. In particular, this result follows if the so-called triangle condition holds.
Keywords
Cite
@article{arxiv.1006.1521,
title = {Upper bound on the expected size of intrinsic ball},
author = {Artem Sapozhnikov},
journal= {arXiv preprint arXiv:1006.1521},
year = {2010}
}