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

Published online by Cambridge University Press:  20 November 2018

Neal Madras
Neal Madras*
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3 e-mail: madras@mathstat.yorku.ca
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Abstract

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For an $N$-step self-avoiding walk on the hypercubic lattice ${{Z}^{d}}$, we prove that the meansquare end-to-end distance is at least ${{N}^{4/(3d)}}$ times a constant. This implies that the associated critical exponent $v$ is at least $2/(3d)$, assuming that $v$ exists.

Keywords

82B4160D0560K35self-avoiding walkcritical exponent
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 113 - 118
Copyright
Copyright © Canadian Mathematical Society 2014

References

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