Towards optimal spectral gaps in large genus
Michael Lipnowski, Alex Wright
Abstract
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.
Topics & Concepts
GenusInfinityEigenvalues and eigenvectorsZero (linguistics)MathematicsLaplace operatorCombinatoricsPure mathematicsMathematical analysisPhysicsBiologyZoologyPhilosophyQuantum mechanicsLinguisticsGeometric and Algebraic TopologyMathematical Dynamics and FractalsGeometry and complex manifolds