6 problems

Let $D(r)$ be a structure function of the form specified in the source, and let $f$ be a Bernstein function, meaning that $f\colon(0,\infty)\to\mathbb{R}$ is smooth, nonnegative, a…

Let $\mathcal{D}_\infty$ denote the class of structure functions under consideration, and let Assumption 3 be the technical condition imposed in the analysis of non-isotropic Gauss…

The paper considers Gaussian random fields on compact metric graphs, with Markov order measured through locality of the associated precision operator and isotropy defined using met…

The critical-threshold conjecture. The supremum is attained in the limit $t,s\to0$ with $t\ne s$, and

Let $X(u)$ be a Gaussian random field, and let $X_{\mathrm{max}}=\max_{u\in M}X(u)$. Write $\mathbb{P}_{\mathrm{tube}}(X_{\mathrm{max}}>c)$ for the tube-method approximation to…

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 $x$…