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 Electronic Communications in Probability > Vol. 15(2010) > Paper 28 open journal systems 


Upper bound on the expected size of the intrinsic ball

Artem Sapozhnikov, EURANDOM


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.


Full text: PDF

Pages: 297-298

Published on: July 23, 2010
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Electronic Communications in Probability. ISSN: 1083-589X