Mesoscopic edge fluctuations for LUE and universality

by Wenkui Liu (KTH)

Thursday 13 Mar 2025, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

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. If time permits, I will also explain how the same technique can be extended to study the global fluctuations of the lozenge tilings.