Welcome to Non-Hermitian random matrix models, a course hosted by the Taught Course Center of Bath-Bristol-Imperial-Oxford-Warwick and Swansea. This page summarizes all key information of the module and contains all course materials, most importantly our weekly schedule.
Key organizational information:
Instructor: Thomas Bothner
Office: 2A.15, Fry Building
Contact: thomas.bothner@bristol.ac.uk and +44 117 455 2070
Meeting times: Mondays 09:30-11:30, starting January 20th, 2025 via Microsoft TEAMS
There is no exam for this course. If you are taking the module for credit you must complete the posted reading assignment and email me your report in LaTeX typeset by the due date written on the assignment sheet. Please let me know if you wish to earn credit for this module!
This course is offered exclusively to PhD students and Postdocs at the Universities of Bath, Bristol, Oxford, Warwick, Swansea and Imperial College London. If you are eligible and interested in this course please sign up via tcc@maths.ox.ac.uk with your MS Teams email address or contact me directly if there are any issues. The course will run for 8 consecutive weeks, see the weekly schedule below.
Course materials (click the links):
Welcome to Non-Hermitian random matrix models - Introductory Slides
Lecture Notes (version Mar 7th - let me know about typos)
Reading assignments (TBD)
Weekly schedule:
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Week 1, January 20th, 2025 from 09:30-11:30 Bristol time:
Topics: Introduction (threefold way), GinUE eigenvalue PDF and correlations
Materials: Lesson Notes
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Week 2, January 27th, 2025 from 09:30-11:30 Bristol time:
Topics: GinUE correlations, elliptic GinUE, induced GinUE, complex spherical ensemble
Materials: Lesson Notes
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Week 3, February 3rd, 2025 from 09:30-11:30 Bristol time:
Topics: Sub-block models, product models, distribution of eigenvalue moduli
Materials: Lesson Notes
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Week 4, February 10th, 2025 from 09:30-11:30 Bristol time:
Topics: Counting functions, smooth linear statistics, thinned GinUE
Materials: Lesson Notes
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Week 5, February 17th, 2025 from 09:30-11:30 Bristol time:
Topics: Configuration integral, sum rules, normal matrix models (part 1)
Materials: Lesson Notes
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Week 6, February 24th, 2025 from 09:30-11:30 Bristol time:
Topics: Normal matrix models (part 2), eigenvalue PDF in the GinSE, skew-orthogonality
Materials: Lesson Notes
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Week 7, March 3rd, 2025 from 09:30-11:30 Bristol time:
Topics: Correlations functions and sum rules, elliptic GinSE, partition functions
Materials: Lesson Notes
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Week 8, March 10th, 2025 from 09:30-11:30 Bristol time:
Topics: Eigenvalue PDF for GinOE, skew-orthogonal polynomials, correlations for real eigenvalues
Materials: Lesson Notes