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Regularized limit of determinants for di...
Vertman, Boris...

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Regularized limit of determinants for discrete tori by Vertman, Boris ( Author )
Lemonjar Open Access
N.A
16-02-2015
We consider a combinatorial Laplace operator on a sequence of discrete graphs which approximates the m-dimensional torus when the discretization parameter tends to infinity. We establish a polyhomogeneous expansion of the resolvent trace for the family of discrete graphs, jointly in the resolvent and the discretization parameter. Based on a result about interchanging regularized limits and regularized integrals, we compare the regularized limit of the log-determinants of the combinatorial Laplacian on the sequence of discrete graphs with the logarithm of the zeta determinant for the Laplace Beltrami operator on the m-dimensional torus. In a similar manner we may apply our method to compare the product of the first N non-zero eigenvalues of the Laplacian on a torus (or any other smooth manifold with an explicitly known spectrum) with the zeta-regularized determinant of the Laplacian in the regularized limit as N goes to infinity.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1502.04541
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