Course Archives Theoretical Statistics and Mathematics Unit
Course: Special Topics 2: Random walk on graphs
Level: Postgraduate
Time: Currently not offered
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.

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Past Exams
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