English

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}
}