Related papers: Benford's law and complex atomic spectra
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions of electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also…
Benford's Law states that the frequency of first digits of numbers in naturally occurring systems is not evenly distributed. Numbers beginning with a 1 occur roughly 30\% of the time, and are six times more common than numbers beginning…
We show that the critical magnetic fields at which a few-electron quantum dot undergoes transitions between successive values of its angular momentum (M), for large M values follow a very simple power-law dependence on the effective…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $P(d)=\log_{10}(1+1/d)$, $d=1,2,\dots,9$. In this paper, we…
We provide general expressions for the joint distributions of the $k$ most significant $b$-ary digits and of the $k$ leading continued fraction coefficients of outcomes of an arbitrary continuous random variable. Our analysis highlights the…
The nuclear electric polarizability is theoretically analyzed using a sum rule derived from the longitudinal part of the forward Compton amplitude. Beyond the leading dipole contribution, this approach leads to the presence of…
We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…
We study, numerically and experimentally, the momentum distribution of atoms cooled in optical lattices. Using semi-classical simulations, we show that this distribution is bimodal, made up of a central feature corresponding to "cold",…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
The coherent quantum dynamics of an electron in the quantum-dot ring structure under the resonant electromagnetic pulse is studied theoretically. A possibility of the selective electron transfer between any two dots is demonstrated. The…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal…
Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be…
In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…
We investigate Benford's law in relation to fractal geometry. Basic fractals, such as the Cantor set and Sierpinski triangle are obtained as the limit of iterative sets, and the unique measures of their components follow a geometric…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast…