Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields

Leonardo Maini, Ivan Nourdin

Let $B=(B_x{)}_{x\in {\mathbb{R}}^d}$ be a collection of $N(0,1)$ random variables forming a real-valued continuous stationary Gaussian field on ${\mathbb{R}}^d$, and set $C(x-y)=\mathbb{…