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This document discusses calculating the asymptotic properties of the discrete Laplacian on a hypercube in D dimensions. It uses the Euler-Maclaurin formula to approximate the heat kernel of the discrete Laplacian. This results in an expansion composed of terms with coefficients that are integrals involving exponential and trigonometric functions. It defines the asymptotic part of this expansion and states the main theorem, which asserts that the difference between the heat kernel and asymptotic part, integr

Author

nicoliere

Language

EN