Random Matrix Theory 

Welcome to the second part of Random Matrix Theory, MATH30033, a module for undergraduate students in year 3 at the University of Bristol. This page summarizes all key information and contains most course materials, most importantly our weekly schedule.

Key organizational information:

This course will be taught in a traditional fashion: you will acquire new theoretical knowledge in the classroom where we will focus foremost on concepts and proof ideas. Content reaches you through lecture notes, in-class lesson notes and Blackboard learning materials. Further details, including learning outcomes and assessment criteria, are summarized in the syllabus. 

Please familiarize yourself with the unit description, click here for MATH30033 in 2024. Please note that this unit has been upgraded from its previous 10cp version, it now runs for 12 weeks in TB2 and is worth 20cp. Part 1 of the module (weeks 13-18) will be taught by Francesco Mezzadri, part 2 (weeks 19-24) by Thomas Bothner. See also our Blackboard page for further organizational information.

Course materials (click the links):

Weekly schedule: (Office Hour=OH, Class=C)

------------------------------------------------------------------------------------------------------------------

Week 19, March 4th - March 8th: 

Topics: Background material: counting measure, linear statistic, generating functional, cluster functions, Gaussian ensembles, variance estimates (page 4-22 in the lecture notes)

Do: Exercise sheet 6, to be submitted by Mar. 8th at noon via Blackboard

Meet: OH, Mar. 7th (13:00-14:00); C, Mar. 5th (15:00-16:00), Mar. 6th (11:00-12:00), Mar. 7th (12:00-13:00)

------------------------------------------------------------------------------------------------------------------

Week 20, March 11th - March 15th: 

Topics: Gaussian unitary ensemble: bulk of the spectrum, semicircle law, edges of the spectrum (page 28-36 in the lecture notes)

Do: Exercise sheet 7, to be submitted by Mar. 15th at noon via Blackboard

Meet: OH, Mar. 14th (13:00-14:00); C, Mar. 12th (15:00-16:00), Mar. 13th (11:00-12:00), Mar. 14th (12:00-13:00)

------------------------------------------------------------------------------------------------------------------

Week 21, March 18th - March 22nd: 

Topics: Real Wigner matrices, proof of Wigner's semicircle law via moment method (page 37-48 in the lecture notes)

Do: Exercise sheet 8, to be submitted by Mar. 22nd at noon via Blackboard

Meet: OH, Mar. 21st (13:00-14:00); C, Mar. 19th (15:00-16:00), Mar. 20th (11:00-12:00), Mar. 21st (12:00-13:00)

------------------------------------------------------------------------------------------------------------------

Week 22, April 15th - April 19th:

Topics: Maximal eigenvalues for real Wigner matrices, Stieltjes transforms: technical preparations, the GUE semicircle law (pages 51-59 in the lecture notes)

Do: Exercise sheet 9, to be submitted by Apr. 19th at noon via Blackboard

Meet: OH, Apr. 18th (13:00-14:00); C, Apr. 16th (15:00-16:00), Apr. 17th (11:00-12:00), Apr. 18th (12:00-13:00)

------------------------------------------------------------------------------------------------------------------

Week 23, April 22nd - April 26th:

Topics: Stieltjes transforms: the GUE semicircle law, the Marchenko-Pastur law (pages 56-64 in the lecture notes)

Do: Exercise sheet 10, to be submitted by Apr. 26th at noon via Blackboard

Meet: OH, Apr. 25th (13:00-14:00); C, Apr. 23rd (15:00-16:00), Apr. 24th (11:00-12:00), Apr. 25th (12:00-13:00)

------------------------------------------------------------------------------------------------------------------

Week 24, April 29th - May 3rd:

Topics: Revision

Do: Prepare yourself for the written exam

Meet: OH, May 2nd (13:00-14:00); C, Apr. 30th (15:00-16:00), May 1st (11:00-12:00), May 2nd (12:00-13:00)