Upper bound on the expected size of intrinsic ball

Artem Sapozhnikov

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arXiv · 1006.1521

Upper bound on the expected size of intrinsic ball

Artem Sapozhnikov

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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.

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Artem Sapozhnikov. 2010-06-08. Upper bound on the expected size of intrinsic ball. https://arxiv.org/abs/1006.1521

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