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2010 Upper bound on the expected size of the intrinsic ball
Artem Sapozhnikov
Author Affiliations +
Electron. Commun. Probab. 15: 297-298 (2010). DOI: 10.1214/ECP.v15-1553


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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Artem Sapozhnikov. "Upper bound on the expected size of the intrinsic ball." Electron. Commun. Probab. 15 297 - 298, 2010.


Accepted: 23 July 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60135
MathSciNet: MR2670196
Digital Object Identifier: 10.1214/ECP.v15-1553

Primary: 60K35
Secondary: 82B43

Keywords: Chemical distance , Critical percolation , high-dimensional percolation , intrinsic ball , Triangle condition

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