Upper bound on the expected size of intrinsic ball

Details Upper bound on the expected size of intrinsic ball Upper bound on the expected size of intrinsic ball

2010-06-08

arxiv.org/abs/1006.1521v1

Mathematics

Probability

Scientific paper

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.

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