A connection between discrete and regularized Laplacian determinants on fractals

2023/12/22 by Konstantinos Tsougkas, Tsougkas, Konstantinos
Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2312.14802

openalex publication_date 2023/12/22 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28

Abstract

The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish under certain conditions a relationship between the logarithm of the determinant of the discrete graph Laplacian on the sequence of graphs approximating the fractal and the regularized determinant which is defined via help of the spectral zeta function. We then at the end present some concrete examples of this phenomenon.

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