Stochastic Processes on Graphs
Class Times and Locations
- Monday and Wednesday, 2:15PM-3:30PM in Room: Sequoia 200
We will study probabilistic models for large systems
of discrete variables interacting according to general graphs.
Local weak convergence, Gibbs measures on trees,
cavity method and replica symmetry breaking.
Examples include: random k-satisfiability, the
assignment problem, spin glasses, neural networks.
We will use the following lecture notes.
Selected portions of the foollowing texts will be `visited' during the
STAT310A or equivalent (STAT310B or equivalent is also recommended).
What is the figure on the right ?
It is a 3-coloring (green-blue-reed) of a 3-regular tree. This coloring
has two peculiarities: (1) It is proper (no edge has both ends of the
same color); (2) We leave to you the puzzle of finding the second
[Courtesy of Peter Winkler]
This course is oriented towards research in applied probability
with active participation by all the students attending it.
Students are invited for form small groups (ideally 2 people)
and get involved in a small research project. Project suggestions and
relevant references will be provided below.
|Project suggestions [pdf]
|Notes on the Sherrington-Kirkpatrick model [pdf]
|Schedule of presentations [pdf]
|Papers and other materials