Lattice effects in the scaling limit of the two-dimensional self-avoiding walk
Probability
2011-09-15 v1 Mathematical Physics
math.MP
Abstract
We consider the two-dimensional self-avoiding walk (SAW) in a simply connected domain that contains the origin. The SAW starts at the origin and ends somewhere on the boundary. The distribution of the endpoint along the boundary is expected to differ from the SLE partition function prediction for this distribution because of lattice effects that persist in the scaling limit. We give a precise conjecture for how to compute this lattice effect correction and support our conjecture with simulations. We also give a precise conjecture for the lattice corrections that persist in the scaling limit of the lambda-SAW walk.
Keywords
Cite
@article{arxiv.1109.3091,
title = {Lattice effects in the scaling limit of the two-dimensional self-avoiding walk},
author = {Tom Kennedy and Gregory F. Lawler},
journal= {arXiv preprint arXiv:1109.3091},
year = {2011}
}
Comments
18 pages, 4 figures