Abstract view
A Lower Bound for the EndtoEnd Distance of SelfAvoiding Walk


Published:20120622
Printed: Mar 2014
Neal Madras,
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3
Abstract
For an $N$step selfavoiding walk on the hypercubic lattice ${\bf Z}^d$,
we prove that the meansquare endtoend 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.
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]
