The asymptotic determinant of the discrete Laplacian
Mathematical Physics
2007-05-23 v1 math.MP
Probability
Abstract
We compute the asymptotic determinant of the discrete Laplacian on a simply-connected rectilinear region in R^2. As an application of this result, we prove that the growth exponent of the loop-erased random walk in Z^2 is 5/4.
Keywords
Cite
@article{arxiv.math-ph/0011042,
title = {The asymptotic determinant of the discrete Laplacian},
author = {Richard Kenyon},
journal= {arXiv preprint arXiv:math-ph/0011042},
year = {2007}
}
Comments
36 pages, 4 figures, to appear in Acta Mathematica