A timely and comprehensive treatment of random field theory with applications across
diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses …

This paper presents a synthesis on the mathematical work done on level crossings of
stationary Gaussian processes, with some extensions. The main results [(factorial) moments …

We introduce a general method, which combines the one developed by authors in 1997 and
one derived from the work of Malevich,(17) Cuzick (7) and mainly Berman,(3) to provide in …

This paper addresses the asymptotic analysis of sojourn functionals of spatiotemporal
Gaussian random fields with long-range dependence (LRD) in time, also known as long …

Our interest in this paper is to explore limit theorems for various geometric functionals of
excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear …

Abstract Let f: R→ R be a stationary centered Gaussian process. For any R> 0, let ν R
denote the counting measure of {x∈ R∣ f (R x)= 0}. Under suitable assumptions on the …

We establish a central limit theorem for the number of roots of the equation X_N(t)=u when
X_N(t) is a Gaussian trigonometric polynomial of degree N. The case u=0 was studied by …

Abstract We prove a Central Limit Theorem for the number of zeros of random trigonometric
polynomials of the form K^-1/2n=1^Ka_n\cos(nt), being (a_n)_n independent standard …

For a smooth, stationary, planar Gaussian field, we consider the number of connected
components of its excursion set (or level set) contained in a large square of area R 2. The …

We study the nodal intersections number of random Gaussian toral Laplace eigenfunctions
('arithmetic random waves') against a fixed smooth reference curve. The expected …