The asymptotic determinant of the discrete Laplacian

Details The asymptotic determinant of the discrete Laplacian The asymptotic determinant of the discrete Laplacian

2000-11-27

arxiv.org/abs/math-ph/0011042v1

Physics

Mathematical Physics

36 pages, 4 figures, to appear in Acta Mathematica

Scientific paper

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.

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