- Basic ensembles in random matrix theory.
- Statistics of eigenvalues and eigenvectors.
- Coulomb gas and beta-ensembles.
- Invariant ensembles.
- Unitary ensembles and determinantal point processes.
- Orthogonal polynomial method.
- Local and global statistics. Loop equations.
- Dyson's Brownian motion.
- Non-invariant ensembles.
- Semi-circle law.
- Resolvent and combinatorial methods.
- General determinantal point processes and applications.
FSF3624 Random Matrices 7.5 credits
Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3624 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
The goal of the course is to discuss the basic results in random matrix theory and also give some insight into the relation of random matrix theory to other areas, e.g. spectral theory and two-dimensional statistical physics.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics.
A basic knowledge ofintegration theory (e.g. SF 2709 Integration theory), probability theory and functional analysis.
Recommended prerequisites
No information inserted
Equipment
No information inserted
Literature
Handouts and lecture notes. A list of recommended literature will be handed out at the beginning of the course.
For the interested reader, we recommend the following books
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An Introduction to Random Matrices, by Greg Anderson, Alice Guionnet, Ofer Zeitouni
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Topics in Random Matrix Theory, by Terry Tao
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert approach, by Percy Deift
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
- INL1 - Assignments, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Hand in assignments and an oral presentation on some topic related to the course.
Other requirements for final grade
Accepted assignments and an oral presentation.
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle
Add-on studies
No information inserted
Contact
Maurice Duits (duits@kth.se)