## Electronic Communications in Probability

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

Artem Sapozhnikov

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 28, 297-298.

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

https://projecteuclid.org/euclid.ecp/1465243971

Digital Object Identifier
doi:10.1214/ECP.v15-1553

Mathematical Reviews number (MathSciNet)
MR2670196

Zentralblatt MATH identifier
1226.60135

Rights

#### Citation

Sapozhnikov, Artem. Upper bound on the expected size of the intrinsic ball. Electron. Commun. Probab. 15 (2010), paper no. 28, 297--298. doi:10.1214/ECP.v15-1553. https://projecteuclid.org/euclid.ecp/1465243971

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