Scalar curvature and $Q$-curvature of random metrics

Abstract

We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. Next, analogous questions are considered for the scalar curvature in dimension $n>2$, and for the $Q$-curvature of random Riemannian metrics.

The proof of Proposition 3.10 has been corrected