Course Archives Theoretical Statistics and Mathematics Unit

Course: Special Topics 2: Random walk on graphs Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus :The course will review interactions between geometric properties of graphs, and the behaviour of random walks, transition densities, and harmonic functions. Our initial goal will be to cover the following specific topics: Graphs and weighted graphs (Examples and Geometric Properties) Random walks Transition densities and the Laplacian Dirichlet or energy form Green functions, Harmonic functions, Harnack inequalities Isoperimetric inequality, Nash inequality, Poincare inequality Heat Kernel bounds. A prerequisite will be Measure Theoretic Probability. It will be helpful but not essential to have knowledge of material covered in Probabilty III. The syllabus of the course is inspired in part by Martin Barlow's PIMS 2004 summer school syllabus and upcoming book. Suggested Texts : 1. M.T. Barlow's Lecture Notes (Lectures given at RIMS, 2005) 2. T. Kumagai's notes (St.Flour summer school 2010) 3. Reversible Markov Chains and Random Walks on Graphs by David Aldous and Jim Fill. 4. Markov Chains and Mixing Times by David A. Levin, Yuval Peres, and Elizabeth L. Wilmer. Top of the page Past Exams

Midterm 17.pdf Semestral 17.pdf 21.pdf Supplementary and Back Paper Top of the page

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