3 problems

Let $M$ be a compact smooth manifold of dimension $d$ without boundary, and let $\rho_j(u)$ denote the Gaussian kinematic densities … where $H_j$ is the $j$th Hermite polynomial. L…

Let $M$ be a compact smooth $d$-dimensional manifold without boundary, let $K_\lambda$ be the covariance kernel of the Gaussian random wave, and let $\Phi_\lambda$ denote the corre…

Let $X$ be a Gaussian field on a Riemannian manifold whose covariance function satisfies the locally isotropic property with respect to the geodesic distance $d(x,y)$ of points $x$…