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Pré-Publication, Document De Travail Année : 2022

RANDOM COVERS OF COMPACT SURFACES AND SMOOTH LINEAR SPECTRAL STATISTICS

Frédéric Naud
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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.
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Dates et versions

hal-03841764 , version 1 (07-11-2022)

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  • HAL Id : hal-03841764 , version 1

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Frédéric Naud. RANDOM COVERS OF COMPACT SURFACES AND SMOOTH LINEAR SPECTRAL STATISTICS. 2022. ⟨hal-03841764⟩
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