The goal of this student seminar is to understand some properties of random walks, especially on non-commutative groups.
Time: Tuesdays 3-4:20pm
Location: E 312
[FS] | Alex Furman's Survey |
[FRW] | Furstenberg's Survey |
[KL] | Karlsson-Ledrappier |
[KV] | Kaimanovich-Vershik |
[BQ] | Benoist-Quint book |
Date | Speaker | Topic |
---|---|---|
6 Jan 2015 | Rachel Vishnepolsky | Introduction. Recurrence, transience of RWs. |
13 Jan 2015 | Ian Frankel | Law of Large numbers. Central Limit theorem. |
20 Jan 2015 | Bena Tshishiku | Random Walks on groups. Markov operators. |
27 Jan 2015 | Clark Butler | Poisson boundary for RWs. Harmonic functions. |
3 Feb 2015 | Mary He | Furstenberg's theorem: Lebesgue measure is hitting measure for a special RW on a lattice in a Lie group. |
10 Feb 2015 | Yun Yang | Multiplicative Ergodic Theorem following Karlsson-Ledrappier I. |
17 Feb 2015 | Yun Yang | Multiplicative Ergodic Theorem following Karlsson-Ledrappier II. |
24 Feb 2015 | Simion Filip | Entropy. Zero entropy is equivalent to trivial boundary. Shannon-McMillan-Breiman theorem. Differential Entropy. |
3 Mar 2015 | Paul Apisa | Limit theorems in semisimple Lie groups: LLN, CLT, Local CLT (following Benoist-Quint). |
10 Mar 2015 | Steve Lalley | Positive entropy is equivalent to positive drift. |
17 Mar 2015 | Steve Lalley | Examples: Lamplighter groups. |