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.
Citation
Artem Sapozhnikov. "Upper bound on the expected size of the intrinsic ball." Electron. Commun. Probab. 15 297 - 298, 2010. https://doi.org/10.1214/ECP.v15-1553
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