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Operator Theory and Analysis of Infinite Networks

Operator Theory and Analysis of Infinite Networks

Hardcover

General MathematicsProbability & Statistics

ISBN10: 9811265518
ISBN13: 9789811265518
Publisher: World Scientific Publishing Company
Published: Apr 2 2023
Pages: 448
Weight: 1.69
Height: 1.00 Width: 6.00 Depth: 9.00
Language: English

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.

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General Mathematics