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A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension.…
This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish…
This work presents the dynamic properties of charged test particles influenced by the gravitational and electromagnetic fields. Accordingly, in this work, we concentrate on the static and axially symmetric metric containing two quadrupole…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study canonical-equilibrium properties of Random Field $O(n)$ Models involving classical continuous vector spins of $n$ components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…
We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time…
I discuss recent advances in the understanding of non-equilibrium gauge field dynamics in plasmas which have particle distributions which are locally anisotropic in momentum space. In contrast to locally isotropic plasmas such anisotropic…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
We study the local times of a large class of Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. We establish moment estimates and H\"{o}lder conditions for the local times of the Gaussian…
A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply connected conductors, at zero frequency the…
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…
We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe…
The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e. the…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…