Related papers: A note on small probabilities for spherical random…

In this paper we study rare events associated to solutions of elliptic partial differential equations with spatially varying random coefficients. The random coefficients follow the lognormal distribution, which is determined by a Gaussian…

We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive…

Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal…

We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense…

We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small…

We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…

We develop a formulation of the strong deflection limit for the scattering of particles following timelike geodesics in asymptotically flat, static, and spherically symmetric spacetimes. For fixed specific energy, as the angular momentum…

The smallest classically stable Q-balls are, in fact, generically metastable: in quantum theory they decay into free particles via collective tunneling. We derive general semiclassical method to calculate the rate of this process in the…

As an extension of isotropic Gaussian random fields and Q-Wiener processes on d-dimensional spheres, isotropic Q-fractional Brownian motion is introduced and sample H\"older regularity in space-time is shown depending on the regularity of…

This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…

This paper investigate the local times and modulus of nondifferentiability of the spherical Gaussian random fields. We extend the methods for studying the local times of Gaussian to the spherical setting. The new main ingredient is the…

We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing…

We give the random environment version of Mogul'ski\v{\i} estimation in quenched sense.Assume that $\{\mu\}_{n\in\bfN}$ (called environment) is a sequence of i.i.d. random probability measures on $\bfR.$~ Let $\{X_n\}_{n\in\bfN}$ be a…

Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…

Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…

We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin-line bundles of the 2-sphere. In particular,…

We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…

We investigate the Gaussian small ball probabilities with random centers, find their deterministic a.s.-equivalents and establish a relation to infinite-dimensional high-resolution quantization.

The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…