Local ultrametric approximation of graph distance based Laplacian diffusion

Fuente: arXiv
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Autor principal: Bradley, Patrick Erik
Formato: Preprint
Publicado: 2024
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author Bradley, Patrick Erik
author_facet Bradley, Patrick Erik
contents The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauß hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated.
format Preprint
id arxiv_https___arxiv_org_abs_2412_20591
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Local ultrametric approximation of graph distance based Laplacian diffusion
Bradley, Patrick Erik
Analysis of PDEs
Mathematical Physics
35P15
The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauß hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated.
title Local ultrametric approximation of graph distance based Laplacian diffusion
topic Analysis of PDEs
Mathematical Physics
35P15
url https://arxiv.org/abs/2412.20591