Topics in Random Matrix Theory
Timetable:
Term 2: Thursday, 12:00-14:00, Room B3.01
Term 3: Thursday, 11:00-13:00, MS.03 (weeks 1, 2), MS.04 (weeks 4,5)
-All students taking this course are expected to participate in the reading seminar on Stochastic Integrable Systems (Tuesdays, 12:00-13:00, Room B3.02).
Check this page for the seminar's programme.
Announcements
10/01/2013 There will be no lecture on Thursday, 17/01/2013
10/01/2013 Please check this site regularly for updates and lecture notes
24/04/13 There will be no lecture in week 3 of term 3
Provisional Syllabus
1. Determinantal point processes
-Hermitian matrix model, the law of eigenvalues
-Correlation functions, Wigner's semi-circle law
-Extended determinantal point processes - Dyson's Brownian motions
-Universality of the bulk scaling limit
-Free fermion representation and integrability
2. Pfaffian point processes
-Ginibre ensemble, spin variables
-Pfaffians and integrals over anti-commuting variables
-Itzykson-Zuber formula
-De Brujn integrals
-Basic differential geometry of symmetric spaces
-Borodin-Sinclair law for real eigenvalues
-Extended Pfaffian point processes: Ginibre process and interacting particles systems
Bibliography
- Madan Lal Mehta, Random Matrices
- Greg W. Anderson, Alice Guionnet and Ofer Zeitouni, Introduction to Random Matrices
