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

  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 self-avoiding walk, critical exponent
MSC Classifications: 82B41, 60D05, 60K35 show english descriptions Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
Geometric probability and stochastic geometry [See also 52A22, 53C65]
Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
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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