Related papers: The field inside a random distribution of parallel…
A general study of relations between the parameters of two centrally-symmetric Levy distributions, often used for one-dimensional investigation of Bose - Einstein correlations, is given for the first time. These relations of the strength of…
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution…
We study spin dynamics of a normal Fermi liquid taking into account the demagnetizing field produced by the spin system itself. Linear solutions of the spin dynamics equations in the form of standing spin waves in a finite volume of liquid…
We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep…
The field of a point electric dipole in an infinite dielectric is obtained by placing the dipole at the center of a spherical cavity of radius $R$ inside the dielectric and then letting $R\to 0$. The result disagrees with the elementary…
Radiation traversing the observable universe provides powerful ways to probe anisotropy of electromagnetic propagation. A controversial recent study claimed a signal of dipole character. Here we test a new and independent data set of 361…
In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m < p. In…
Temporal broadening of pulsar signals results from electron density fluctuations in the interstellar medium that cause the radiation to travel along paths of different lengths. The Gaussian theory of fluctuations predicts that the pulse…
This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability…
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…
We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting…
We demonstrate that a non-vanishing interaction force exists between pairs of induced dipoles in random, statistically stationary electromagnetic field. This new type of optical binding force leads to long-range interaction between dipolar…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized…
We study the two-dimensional localization problem for (i) a classical diffusing particle advected by a quenched random mean-zero vorticity field, and (ii) a quantum particle in a quenched random mean-zero magnetic field. Through a…
Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.
In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…