Mesoscopic CLT for β-ensembles at intermediary temperature

Gaultier Lambert (KTH, Stockholm)

Apr 15. 2026, 09:00 — 10:00

We investigate β-ensembles with real-analytic potential V in the intermediate temperature regime, 1 >>β>>1/N. We obtain global and mesoscopic CLTs after recentering by a refined equilibrium measure. Our result reveals a transition between random matrix/Poisson regimes in the variance of the fluctuations depending on the mesoscopic scale and the parameter α=βN. Our main technique consists in studying loop equations in this intermediate temperature regime and the proofs involve the construction of an appropriate re-centering which refines the usual equilibrium measure and two optimal local law (one for each regime). 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Random Matrices and Operators (Workshop)
Organizer(s):
Nathanael Berestycki (U of Vienna)
Paul Bourgade (CIMS, New York)
Giorgio Cipolloni (U Tor Vergata, Rome)