Riemann moduli spaces are quantum ergodic

Abstract

In this note we show that the Riemann moduli spaces $M_{g,n}$ equipped with the Weil--Petersson metric are quantum ergodic for $3g+n\ge 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.

15 pages; version 2: minor revisions suggested by referees