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This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies that for a g
Series expansions of isotropic Gaussian random fields on $mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations provide an alternative to the standard Karhunen-Lo`eve expansions of iso
We derive exact asymptotics of $$mathbb{P}left(sup_{tin mathcal{A}}X(t)>uright), ~text{as}~ utoinfty,$$ for a centered Gaussian field $X(t),~tin mathcal{A}subsetmathbb{R}^n$, $n>1$ with continuous sample paths a.s. and general dependence structure, f
We study the total mass of high points in a random model for the Riemann-Zeta function. We consider the same model as in [8], [2], and build on the convergence to Gaussian multiplicative chaos proved in [14]. We show that the total mass of points whi
The tube method or the volume-of-tube method approximates the tail probability of the maximum of a smooth Gaussian random field with zero mean and unit variance. This method evaluates the volume of a spherical tube about the index set, and then trans