no code implementations • 11 Mar 2021 • Paul Bourgade, Krishnan Mody, Michel Pain
In the setting of generic $\beta$-ensembles, we use the loop equation hierarchy to prove a local law with optimal error up to a constant, valid on any scale including microscopic.
Probability Mathematical Physics Mathematical Physics
no code implementations • 4 Jan 2021 • Michel Pain, Delphin Sénizergues
In this paper, we obtain the second and third orders in the asymptotic expansion of the height of weighted recursive trees, under similar assumptions.
Probability 60J80 (Primary) 05C05, 60G70 (Secondary)
