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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

  1. Madan Lal Mehta, Random Matrices
  2. Greg W. Anderson, Alice Guionnet and Ofer Zeitouni, Introduction to Random Matrices

 



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