Random Walks, Conductance, and Resistance for the Connection Graph Laplacian

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-19 DOI:10.1137/23m1595400

Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn, Sawyer J. Robertson, Zhengchao Wan, Yusu Wang

引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1541-1572, September 2024.
Abstract. We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of Dirichlet-type and Poisson-type problems on connection graphs. Additionally, we delve into random walks, taking into account both node transitions and vector rotations. This approach introduces novel concepts of effective conductance and resistance matrices for connection graphs, capturing mean rotation matrices corresponding to random walk transitions. Thereby, it provides new theoretical insights for network analysis and optimization.

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连接图拉普拉卡的随机漫步、传导和阻力

SIAM 矩阵分析与应用期刊》，第 45 卷第 3 期，第 1541-1572 页，2024 年 9 月。摘要。我们研究了连接图中的有效阻力概念，扩展了其在无向图中的传统应用。我们通过关注连接图上的 Dirichlet 型和 Poisson- 型问题的对偶性，提出了连接图中有效阻力的稳健定义。此外，我们还深入研究了随机漫步，将节点转换和向量旋转都考虑在内。这种方法为连接图引入了有效传导矩阵和电阻矩阵的新概念，捕捉到了与随机漫步转换相对应的平均旋转矩阵。因此，它为网络分析和优化提供了新的理论见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.