Lipschitz Lectures

Integrable probability and Macdonald processes

Date: January 9 - 24, 2013
Time: Wednesdays 10 - 12 a.m., Thursdays 9 - 11 a.m.
Location: Lipschitz Lecture Hall, Bonn University, Endenicher Allee 60, Bonn
Office hours: Wednesday and Thursday 3 - 5 p.m. in room 3-040.
Official website

Week 1

Lecture 1: Overview

Slides

Exerices

References

Chapter 1, Symmetric functions and Hall Polynomials, I.G. Macdonald

Chapter 4, The Symmetric Group, B. Sagan

Section 2.1, Macdonald processes, A. Borodin and I. Corwin

Lecture 2: Introduction to symmetric functions, and Schur measure

Notes: Introduction to symmetric functions

Notes: Schur functions

Exerices

References

Lectures on integrable probability, A. Borodin, V. Gorin

Week 2

Lecture 3: Schur processes (determinantal structure and dynamics)processes

Notes: Schur processes

Exerices

References

Determinantal point processes, A. Borodin

Determinantal random point fields, A. Soshnikov

An introduction to random matrices, G. Anderson, A. Guionnet, O. Zeitouni

Lecture 4: Macdonald processes

Notes: Macdonald processes

Exerices

References

Chapter VI, Symmetric functions and Hall Polynomials, I.G. Macdonald

Macdonald processes (Chapters 2 and 3), A. Borodin, I. Corwin

Introduction to q-difference equations, G. Bangerezako

Week 3

Lecture 5: Duality for q-TASEP

Notes: Duality and replica methods

Exerices

References

From duality to determinants for q-TASEP and ASEP, A. Borodin, I. Corwin, T. Sasamoto

Lecture 6: Replicas for SHE, analysis of ASEP, and open problems / conclusion