This is the website for the reading group on Random Matrix Theory that we are holding in the Winter semester 2024/25 in Ljubljana.
The main reference are lecture notes by Roland Speicher.
Each participant chooses a topic and prepares a 45-minute lecture for the group. You do not need to cover the entire material in great detail and it is perfectly fine to focus on explaining the main ideas (after all, you only have 45 minutes).
If you decide to participate, please send an email to urban.jezernik@fmf.uni-lj.si so I can mark the topic as chosen.
A list of topics, along with references, is available here (prepared by Marco Barbieri).
Semicircular distribution and Wick formula. (Andoni Zozaya)
Wigner’s semicircle law: combinatorial proof. (Matjaž Konvalinka)
Wigner matrices and Stieltjes transform. (Urban Jezernik)
Wigner’s semicircle law: analytic proof. (Jaka Smrekar)
Concentration phenomena. (Aleksey Kostenko, Jaka Smrekar)
Eigenvalue distribution for GOE and GUE. (Andoni Zozaya)
Non-crossing paths and Harer–Zagier recursion. (Maruša Lekše)
Tracy–Widom distribution. (Urban Jezernik)
Longest increasing subsequence. (Hans Höngesberg)
The circular law.
Towards free probability. (Franz Lehner)
We meet on Wednesdays at 14-15 in classroom 3.06.
09/10/2024 Marco Barbieri: Introductory meeting [video]
23/10/2024 Andoni Zozaya: Semicircular distribution and Wick formula [video]
06/11/2024 Matjaž Konvalinka: Wigner’s semicircle law: combinatorial proof [video]
13/11/2024 Urban Jezernik: Wigner matrices and Stieltjes transform [video]
20/11/2024 Jaka Smrekar: Wigner’s semicircle law: analytic proof [video]
27/11/2024 Aleksey Kostenko: Concentration phenomena, part 1 [video]
04/12/2024 Jaka Smrekar: Concentration phenomena, part 2 [video]
11/12/2024 Andoni Zozaya: Eigenvalue distribution for GOE and GUE [video]
18/12/2024 Maruša Lekše: Non-crossing paths and Harer–Zagier recursion [video]
08/01/2025 Urban Jezernik: Tracy–Widom distribution
15/01/2025 Franz Lehner: Free probability [video]