Stat 316, Stochastic Processes on Graphs

Amir Dembo, Andrea Montanari, Stanford University, Autumn 2017

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.

This year we will develop the following themes:

  1. Models on sparse, locally tree-like graps. These lecture notes provide some background:

    1. A. Dembo and A. Montanari, Gibbs Measures and Phase Transitions on Sparse Random Graphs (2008 Brazilian School of Probability)

    2. A. Montanari, Statistical Mechanics and Algorithms on Sparse and Random Graphs (2013 St. Flour School of Probability)

  2. The satisfiability phase transition for random constraint satisfaction problems:

    1. J Ding, A Sly, N. Sun, Satisfiability Threshold for Random Regular NAE-SAT

  3. The Sherrington-Kirkpatrick model, mainly following this recent book

    1. D. Panchenko, The Sherrington-Kirkpatrick Model, 2013

Class Times and Locations

  • Tue, Thu 12:00PM - 1:20PM, Green Earth Sciences 131

  • First lecture on September 26

  • No class on November 28