Math 601D Section 201
Entropy and Equilibrium States in Ergodic Theory and Statistical Mechanics

Schedule of student talks

Felipe: Mixing, Mixing of Higher Orders and the 3-dot example

Subhajit: Anosov and Axiom A diffeomorphisms

Qiang: Markov Partitions for Anosov and Axiom A

Saif: Variational Principle

Nishant: Gibbs measures and Equilibrium states

Thomas: Shannon-MacMillan-Breiman Theorem

Ben: Stochastic Dominance and existence of mu^+ for Ising

Spencer: Phase Transitions for the Ising Model

Brian: Ergodic theory of Axiom A diffeomorphisms (Bowen, Chapter 4)

Raimundo: Extremality of Gibbs measures and ergodicity of mu^+ for the Ising model

Course Outline

Another good general reference: Ergodic Theory, by Karl Petersen, Cambridge Press

Lecture Notes 1-3

Lecture Notes 4-6

Lecture Notes 7-9

Lecture Notes 10-12

Lecture Notes 13-15

Lecture Notes 16-17

Lecture Notes 18-20

Lecture Notes 21-23

Lecture Notes 24-26

Lecture Notes 27-29

Lecture Notes 30-32

Lecture Notes 33-34

Lecture Notes 35-36

The horseshoe

The solenoid

Proof of Z^d ergodic theorem (from Keller)

Entropy Inequalities

Running List of Ergodic theory exercises I (updated January 25)

Problem Session: Thursday, Feb. 12, 5:30-7:30, Math 126

Running List of Ergodic theory exercises II (updated March 5)

Survey article on applications of ergodic theory to combinatorial number theory (Vitaly Bergelson)

Suggested topics for talks

Some papers related to student talk topics:

B. Cipra, Introduction to the Ising Model

T. de la Rue, 2-fold and 3-fold mixing: . . .

H-O. Georgii, O. Haggstrom, C. Maes, The random geometry of equilibrium phases

T. Ward, Lecture Notes on Z^d dynamical systems (with some interesting examples)