Course Archives    Theoretical Statistics and Mathematics Unit

Course:Analysis on Graphs Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: Review of Matrices and Graphs. Incidence matrix, Adjacency matrix and Laplace matrix of a graph. The Laplace operator on graphs. Random walks on graphs. Dirichlet Problem. Spectral properties. Eigenvalues and mixing time. Cheeger’s inequality. Eigenvalues on infinite graphs. Estimates of the heat kernel. CarneVaropoulous bound. Reference Texts: 1. R. B. Bapat: Graphs and Matrices. 2. A. Grigor’yan.: Introduction to Analysis on Graphs. 3. M. T. Barlow: Random Walks and Heat Kernel on Graphs. 4. R. Lyons and Y. Peres: Probability on trees and networks. Top of the page Past Exams Top of the page

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