# Scalar Curvature and Q-Curvature of Random Metrics

```@article{Canzani2010ScalarCA,
title={Scalar Curvature and Q-Curvature of Random Metrics},
author={Yaiza Canzani and Dmitry Jakobson and Igor Wigman},
journal={The Journal of Geometric Analysis},
year={2010},
volume={24},
pages={1982-2019}
}```
• Published 29 January 2010
• Mathematics
• The Journal of Geometric Analysis
We define a family of probability measures on the set of Riemannian metrics lying in a fixed conformal class, induced by Gaussian probability measures on the (logarithms of) conformal factors. We control the smoothness of the resulting metric by adjusting the decay rate of the variance of the random Fourier coefficients of the conformal factor. On a compact surface, we evaluate the probability of the set of metrics with non-vanishing Gauss curvature, lying in a fixed conformal class. On higher…
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