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# A Lower Bound for the End-to-End Distance of Self-Avoiding Walk

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Published:2012-06-22
Printed: Mar 2014
• Neal Madras,
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3
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## Abstract

For an $N$-step self-avoiding walk on the hypercubic lattice ${\bf Z}^d$, we prove that the mean-square end-to-end distance is at least $N^{4/(3d)}$ times a constant. This implies that the associated critical exponent $\nu$ is at least $2/(3d)$, assuming that $\nu$ exists.
 Keywords: self-avoiding walk, critical exponent
 MSC Classifications: 82B41 - Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 60D05 - Geometric probability and stochastic geometry [See also 52A22, 53C65] 60K35 - Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

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