Expected number of nodal components for cut‐off fractional Gaussian fields
Expected number of nodal components for cut‐off fractional Gaussian fields
Let $({\mathcal{X}},g)$ be a closed Riemmanian manifold of dimension $n>0$. Let $\Delta$ be the Laplacian on ${\mathcal{X}}$, and let $(e\_k)\_k$ be an $L^2$-orthonormal and dense family of Laplace eigenfunctions with respective eigenvalues $(\lambda\_k)\_k$. We assume that $(\lambda\_k)\_k$ is non-decreasing and that the $e\_k$ are real-valued. Let $(\xi\_k)\_k$ be a sequence …