RANDOM COVERS OF COMPACT SURFACES AND SMOOTH LINEAR SPECTRAL STATISTICS
Résumé
We consider random n-covers of an arbitrary compact
hyperbolic surface X. We show that in the large n regime and small window limit, the variance of the smooth spectral statistics of the Laplacian twisted by a unitary abelian character, obey the universal laws of GOE and GUE random matrices, depending on wether the character preserves or breaks the time reversal symmetry. We also prove a generalization for higher dimensional twists valued in compact linear groups.
These results confirm a conjecture of Berry and is a discrete analog of a recent work of Rudnick for the Weil-Petersson model of random surfaces.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)