Description

Book Synopsis
Explores the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk on finite graphs.

Table of Contents
  • The Laplace operator on graphs
  • Spectral properties of the Laplace operator
  • Geometric bounds for the eigenvalues
  • Eigenvalues on infinite graphs
  • Estimates of the heat kernel
  • The type problem
  • Exercises
  • Bibliography
  • Index

    Introduction to Analysis on Graphs

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      A Paperback by Alexander Grigor`yan

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 10/30/2018 12:00:00 AM
        ISBN13: 9781470443979, 978-1470443979
        ISBN10: 147044397X

        Description

        Book Synopsis
        Explores the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk on finite graphs.

        Table of Contents
        • The Laplace operator on graphs
        • Spectral properties of the Laplace operator
        • Geometric bounds for the eigenvalues
        • Eigenvalues on infinite graphs
        • Estimates of the heat kernel
        • The type problem
        • Exercises
        • Bibliography
        • Index

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