Abstract: I will consider a class of random matrices X with the ‘shape’ of Young diagrams λ. I will show that when the Young diagrams are 'block-shaped’ (dilations of staircase partitions), the empirical spectral distribution of XX* converges to a distribution whose moments are a generalisation of the Catalan numbers and have a precise combinatorial interpretation. I will also discuss several properties of the limiting distribution. Special cases are the Marchenko-Pastur and Dykema-Haagerup distributions of square and triangular random matrices, respectively.
Based on a joint work with Marilena Ligabò and Tommaso Monni.
Random matrices associated to Young diagrams
03.10.2023 14:00 - 15:00
Organiser:
M. Lis
Location:
TU Wien, EI 11 Geodäsie HS, Gußhausstraße 27-29