Mathematics 275: Probability Theory and Stochastic Processes

Mathematics 275B - Winter 2007

• Time and place: MWF at 11 in WGYoung 1044
• Instructor: Thomas M. Liggett
• Office hours: MWF 2-3 in MS 7919 (I will often be available at 3 as well, so if you have a conflict 2-3 and would like to see me at 3, let me know during the class that day)
• Text: Probability: Theory and Examples, 3rd edition, by R. Durrett
• Topics: (a) Random Walks, (b) Martingales, (c) Additive and Subadditive Ergodic Theory, and possibly (d) (depending on students' background) Markov Chains.
• Grades will be based on homework to be assigned from Durrett's book and the final exam (March 22, 11:30-2:30). If you choose S/U grading on the Registrar's page, the final exam is optional.
• I will begin our treatment of random walks on January 8. The lectures on January 10 and 12 will be given by Marek Biskup. He will finish up his treatment of stable and infinitely divisible laws, and their domains of attraction. January 15 is a holiday, so we will continue with random walks on Wednesday, January 17.

Assignments

• Due January 24: Page 159 #7.8 (you may use the result of #7.7); pages 174-175 # 1.2,1.4,1.6,1.7.
• Due February 5: Pages 179-180 #1.12,1.14,1.15; pages 218-223 #1.1,1.2,1.3,1.4; problem A: Let U_n be a random walk on Z^d, and V_n be an independent copy of U_n. Let S_n=U_n-V_n be the symmetrization. Prove: If S_n is transient, then so is U_n.
• Due February 26: Pages 225-235 #1.6,1.9,1.10 (use conditioning!),1.12,2.2,2.4,2.9,2.11.
• Due March 14: Pages 237-268 #3.1,4.5,4.8,4.9,5.7,6.4; pages 335-337 #1.3,1.6.