# Julian Mauersberger: Large gap asymptotics for determinantal point processes

**Time: **
Fri 2019-11-22 15.45 - 16.05

**Location: **
KTH, D3

**Participating: **
Julian Mauersberger, KTH

### Abstract

I will present joint work with Christophe Charlier and Jonatan Lenells on the large gap asymptotics of certain determinantal point processes. Such point processes often arise as extreme eigenvalue distributions of random matrix ensembles. We are particularly interested in the probability that there is no eigenvalue on an interval \([0, s]\), the so-called gap probability at the hard edge, as the size of the matrix approaches infinity. It turns out that the large gap asymptotics, i.e. the asymptotic behavior of the gap probability as the parameter \(s\) becomes large, can be studied via tools of complex analysis. By applying such tools, we compute the constant terms in the large gap asymptotics for two types of point processes. Deriving similar constants has a long history in random matrix theory.