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.

• M.T. Barlow's Lecture Notes (Lectures given at RIMS, 2005)
• T. Kumagai's notes (St.Flour summer school 2010)

• Reversible Markov Chains and Random Walks on Graphs by David Aldous and Jim Fill.
• Markov Chains and Mixing Times by David A. Levin, Yuval Peres, and Elizabeth L. Wilmer.

• Random Walk and Electrical Networks by Rajat Hazra

• 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 January 5th Class January 10th Class January 12th Class January 13th Class January 19th Class January 20th Class February 3rd Class February 9th Class February 10th Class February 16th Class , part 2 March 3rd Class March 16th Class March 17th Class

  Homework Sets Homework 1 20th Jan 2017 Homework 2 27th Jan 2017 Homework 3 4th Feb 2017 Homework 4 10th Feb 2017 Homework 5 March 10th 2017 Homework 6 March 24th 2017 Homework 7 Aoril 6th 2017 Homework 8 April 13th 2017 Homework 9 April 18th 2017

  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]