The asymptotic determinant of the discrete Laplacian

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56677We 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 MathematicaMathematical PhysicsProbability82B20; 60J15The asymptotic determinant of the discrete Laplaciantext