# Graduate seminar: topics in discrete probability. Tel Aviv university, Fall 2015

**
Thursday 4 - 6 pm **

Room: Schreiber 209

We will study some contemporary papers in discrete probability. In an attempt to be diverse we will study papers dealing with Markov chains and mixing, percolation, combinatorics, geometric group theory and even some computer science (efficient sampling). Below is a list of papers we plan to discuss - ideally each student will give a 2 hour talk on one of the papers.
On the first meeting I will provide an introduction and survey of some of the papers and discuss some organizational matters.
### Location

Thursday 4 - 6 pm, Schreiber 209
### Prerequisites

Undergraduate probability.
### List of papers

- Compositions of random transpositions, by O. Schramm.
- Emergence of giant cycles and slowdown transition in random transpositions and k-cycles, by N. Berestycki.
- Cycle density in infinite Ramanujan graphs, by R. Lyons and Y. Peres.
- Cutoff on all Ramanujan graph, by E. Lubetzky and Y. Peres.
- Amenability via random walks, by L. Bartholdi and B. Virag.
- Poisson Boundaries of Lamplighter Groups: Proof of the
Kaimanovich-Vershik Conjecture, by R. Lyons and Y. Peres.
- Percolation on the hyperbolic plane, by I. Benjamini and O. Schramm.
- Percolation and local isoperimetric inequalities, by A. Teixeira.
- Kestenâ€™s theorem for Invariant Random
Subgroups, by M. Abert, Y. Glasner and B. Virag.
- Mean field conditions for coalescing random walks, by R. I. Oliviera.
- Coupling from the past (chapter 22), by Propp and Wilson.

For organizational matters and participation please contact Asaf Nachmias.