CS294-204: Phase Transtions

INSTRUCTOR: Christian Borgs (borgs@eecs)
TIME: Tuesday, Thursday 12:30-2:00
PLACE: Soda 310
OFFICE HOURS: Wednesday, 1:30-2:30, Thursday, 2:15 - 3:15



Phase transitions are ubiquitous in physics and many other real-world systems, but can also be found in many areas of computer science and combinatorics, from the classical phase transition involving the appearance of a giant component in random graphs, to transitions from fast to slow convergence of randomized (e.g., Monte Carlo) algorithms, to phase transitions in random satisfiability formulas, to thresholds for learning models from sparse data. In this class, we will study these phase transitions using methods from mathematical physics, combinatorics, and computer science. In addition, I will also cover the topic of convergence for sparse graphs, known as local weak convergence and its relation to graphical models on such sequences.

Since several of the topics covered in this class are drawn from the recent research literature, the is no single book covering the material of this class. For some of the earlier topics involving branching processes, random graphs, and SIR epidemics, I will roughly follow Chapters 2 and 3 of Durrett’s book Random Graph Dynamics, while the methods from statistical physics used in later classes are based on a CBMS lecture series I gave in Memphis many years ago (I will make chapters of my yet to be finished book on this subject available during the class). Additional literature, including original research papers, will be provided during the course.


The course is open to graduate students with a strong mathematical background / good level of mathematical maturity (similar to that for graduate classes in mathematics, statistics, or theoretical computer science).

Tentative List of Topics

A first look at Phase Transitions: Expansion Methods 1: Expansion Methods 2: Computer Science and Learning:


SYLLABUS (First few lectures)