On the large genus asymptotics of psi-class intersection numbers

Abstract

Based on an explicit formula of the generating series for the $n$-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [9] regarding the large genus uniform leading asymptotics of the psi-class intersection numbers. We also investigate polynomiality phenomenon in the large genera.

Corrected a mistake in Lemma 8; added the proof of the identity (54); added a few more details. 35 pages