M.Math II (Special Topics Course): Random Walk on Graphs Semester II 2016-17
http://www.isibang.ac.in/~athreya/rgw
Instructor: Siva Athreya
Office: A 12.
Course 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.
References:
Random Walk of Graphs
Markov Chains
Other Courses
Some Classic or otherwise articles
- Foster's Original Paper (See Class photos of 20th January pages 17-23 on Foster's Criterion.)
E-Mail: My e-mail address is athreya AT isibang DOT ac DOT in. Please send me an email, from an account that you use regularly, so that I can put you on the class list.
Classes : Thursday 9:55-10:55am, 2-3pm and 4:15-5:15pm, Friday 2-3pm. Semester Calendar
Class Board Photos
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Scoring: Midterm 1 is worth 30 % of the grade. Final exam is worth 50 % of the grade. The Homework will consist of 20 % of the grade.
[Probability I home page]
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