Explicit spectral gaps for random covers of Riemann surfaces

DOI10.1007/s10240-020-00118-wOpenAlexW3038057161WikidataQ104602149 ScholiaQ104602149MaRDI QIDQ827017

Frédéric Naud, Michael Magee

Publication date: 6 January 2021

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.00658

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Diffusion processes and stochastic analysis on manifolds (58J65)

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Cites Work

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• Resonances and density bounds for convex co-compact congruence subgroups of \(\mathrm{SL}_2(\mathbb Z)\)
• Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve
• Expansion of random graphs: new proofs, new results
• Mathematical study of scattering resonances
• Wave decay on convex co-compact hyperbolic manifolds
• Poisson-Dirichlet distribution for random Belyi surfaces
• The spectral geometry of a tower of coverings
• Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
• Spectre du Laplacien, graphes et topologie de Fell. (Spectrum of the Laplacian, graphs and Fell topology)
• Ramanujan graphs
• Eigenvalues and expanders
• The isoperimetric number of random regular graphs
• On decay of correlations in Anosov flows
• Hausdorff dimension of quasi-circles
• On the second eigenvalue of a graph
• The limit set of a Fuchsian group
• Relative expanders or weakly relatively Ramanujan graphs.
• The Selberg zeta function for convex co-compact Schottky groups
• On the spectral gap for infinite index ``congruence subgroups of SL\(_2(\mathbb{Z})\)
• Dolgopyat's method and the fractal uncertainty principle
• Spectral gaps without the pressure condition
• Euclidean algorithms are Gaussian
• The divisor of Selberg's zeta function for Kleinian groups. Appendix A by Charles Epstein
• Upper bounds on the number of resonances for non-compact Riemann surfaces
• Decay of correlations
• Quantitative spectral gap for thin groups of hyperbolic isometries
• Large degree covers and sharp resonances of hyperbolic surfaces
• Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy
• Fractal uncertainty principle with explicit exponent
• Uniform congruence counting for Schottky semigroups in \(\mathrm{SL}_2(\mathbb{Z})\)
• Eigenvalues of random lifts and polynomials of random permutation matrices
• Fourier dimension and spectral gaps for hyperbolic surfaces
• Density and location of resonances for convex co-compact hyperbolic surfaces
• Random construction of Riemann surfaces
• Expanding maps on Cantor sets and analytic continuation of zeta functions
• A proof of Alon’s second eigenvalue conjecture and related problems
• Small eigenvalues of surfaces of finite type
• Fractal Uncertainty for Transfer Operators
• An introduction to fractal uncertainty principle
• Measure preserving words are primitive
• Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$
• Spectral theory of infinite-area hyperbolic surfaces