Patterson-Sullivan and Wigner distributions of convex-cocompact hyperbolic surfaces

2024/11/29 by Delarue, Benjamin, Palmirotta, Guendalina
#58C40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2411.19782

Abstract

We prove that the Patterson-Sullivan and Wigner distributions on the unit sphere bundle of a convex-cocompact hyperbolic surface are asymptotically identical. This generalizes results in the compact case by Anantharaman-Zelditch and Hansen-Hilgert-Schröder.

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