A central limit theorem for the number of excursion set components of Gaussian fields

Dmitry Beliaev, Michael McAuley, Stephen Muirhead

For a smooth stationary Gaussian field on ${\mathbb{R}}^d$ and level $\ell \in \mathbb{R}$, we consider the number of connected components of the excursion set $\{f\ge \ell \}$ (or l…