The asymptotic determinant of the discrete Laplacian
Abstract
Description
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.
36 pages, 4 figures, to appear in Acta Mathematica
36 pages, 4 figures, to appear in Acta Mathematica