Stanford
      University Stats 316
Stochastic Processes on Graphs
Spring 2010

Course Information

                                               
                                               

Class Times and Locations

  • Monday and Wednesday, 2:15PM-3:30PM in Room: Sequoia 200

Course Description

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.

References

We will use the following lecture notes. Selected portions of the foollowing texts will be `visited' during the course.

Prerequisites

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 peculiarity. [Courtesy of Peter Winkler]

Instructors

Grading

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.

Handouts

Handout Posted
Syllabus [pdf] 3/27
Project suggestions [pdf] 3/27
Notes on the Sherrington-Kirkpatrick model [pdf] 4/12
Schedule of presentations [pdf] 5/27

Papers and other materials