## Random Matrices,

Summer term 2018

Place and Time

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Time: |
Place: |
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Lecture (VO) 2 hrs. | Mon 13:15-14:45 | SR10 | 5.3. |

Content

- Random Hermitian matrices, Unitary ensambles, GUE, Wigner semicircle law for GOE, [1]
- Unitary ensambles, spectral variables, distribution of eigenvalues [2, Chap 5]
- Equilibrium measures, scaling, variational problem, equilibrium measure for the Gaussian case [2, Chap 6]
- Riemann-Hilbert problems (RHP), Sokhotski-Plemelj formula, the RHP for orthogonal polynomials [2, Chap 1,3]
- RHPs in the precise sense, deformation of a RHP, some analytic considerations of RHPs, construction of the parametrix [2, Chap 7]

Target audience

Module "Electives in Analysis (MANV)" in the Master's programme in Mathematics.

Assessment

The course assessment for the lecture will be via an oral examination at the end of
the course.

Literature

Some textbooks:

Looking forward to seeing you, Gerald Teschl
- G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices, Cambridge, 2010.
- P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Amer. Math. Soc, 2000
- A. Its, Large N Asymptotics in Random Matrices: The Riemann-Hilbert Approach, in "Random Matrices, Random Processes and Integrable Systems", J. Harnad (ed), Springer, 2011
- P. van Moerbeke, Random and Integrable Models in Mathematics and Physics, in "Random Matrices, Random Processes and Integrable Systems", J. Harnad (ed), Springer, 2011
- L. Pastur and M. Shcherbina, Eigenvalue Distribution of Large Random Matrices, Amer. Math. Soc, 2011
- F. Rezakhanlou, Lectures on Random Matrices, Lecture notes
- Terence Tao, Topics in random matrix theory, AMS, 2012.