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

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

We apply Brunetti and Fredenhagen's [Phys. Rev. A 66 (2002) 044101] concept of the time of occurrence of an event in quantum mechanics to the example of scattering off a spherical potential. Thereby, we re-derive the expression of…

We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…

In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…

We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on…

The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…

Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets…

We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…

In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

We derive laws of the iterated logarithm for random walks on random conductance models under the assumption that the random walks enjoy long time sub-Gaussian heat kernel estimates.

We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers…

This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…

Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part…

In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…

We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…

We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…