A random cover of a compact hyperbolic surface has relative spectral gap 316-ε

• Published in: Geometric and functional analysis Vol. 32; no. 3; pp. 595 - 661
• Main Authors: Magee, Michael, Naud, Frédéric, Puder, Doron
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2022; Springer Nature B.V
• Subjects: Analysis; Eigenvalues; Mathematics; Mathematics and Statistics

Let X be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature - 1 . For each n ∈ N , let X n be a random degree- n cover of X sampled uniformly from all degree- n Riemannian covering spaces of X . An eigenvalue o...