4 papers · 1 filter
Randomly twisted transfer operators and singular values statistics
Frédéric Naud
In this paper, we investigate the singular values of a natural family of transfer operators twisted by large random permutation matrices. In the large N limit, we obtain a Weyl law…
Spectral Gaps on Large Hyperbolic Surfaces
Laura Monk, Frédéric Naud
In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the inve…
On the spectral gap of negatively curved surface covers
Will Hide, Julien Moy, Frederic Naud
Given a negatively curved compact Riemannian surface , we give an explicit estimate, valid with high probability as the degree goes to infinity, of the first non-trivial eigenva…
Spectral gap for random Schottky surfaces
Irving Calderón, Michael Magee, Frédéric Naud
We establish a spectral gap for resonances of the Laplacian of random Schottky surfaces, which is optimal according to a conjecture of Jakobson and Naud.