6 papers
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…
Asymptotics of zeta determinants of Laplacians on large degree abelian covers
Nguyen Viet Dang, Jiasheng Lin, Frédéric Naud
Let be some smooth, closed, compact Riemannian manifold and be an increasing sequence of large degree cyclic covers of that converges when $N\rightar…
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.
Random covers of compact surfaces and smooth linear spectral statistics
Frédéric Naud
We consider random n-covers of an arbitrary compact hyperbolic surface . We show that in the large n regime and small window limit, the variance of the smooth spectral sta…