Mesoscopic edge fluctuations for LUE and universality
A talk in the Seminar Zufallsmatrizen series by
Wenkui Liu
| Abstract: | Mesoscopic fluctuations for orthogonal polynomial ensembles have been studied in the literature since 2000. However, most works focus on the bulk, and less is known about the edges. In this talk, I am reporting on our recent work on the mesoscopic edge universality of orthogonal polynomial ensembles arXiv:2501.14422. I will present the main theorems and the ideas of the proof with an example of Laguerre Unitary Ensemble (LUE). The interesting aspect of LUE is that it presents both hard and soft edges. Our approach reveals how the different types of edges of LUE affect the mesoscopic fluctuations. Universality comes naturally from our approach. The main tool used in this study is the three-term recurrence relation of the associated orthogonal polynomials. Within the CRC this talk is associated to the project(s): C6 |