Towards optimal spectral gaps in large genus

By Michael Lipnowski, A. Wright. Annals of Probability, 2021

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We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than $3/16-\epsilon$ goes to zero as the genus goes to infinity.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ee9244515ca7372c8cfc243beb85d7bb3fc13e0b