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A Lower Bound for the End-to-End Distance of Self-Avoiding Walk |
6 pages
Published:2012-06-22
- Neal Madras,
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] |