Related papers: Factorial Moments in Complex Systems
The negative binomial distribution NB$(k,r)$ of Type I is the probability distribution for a sequence of independent Bernoulli trials (with success parameter $p\in(0,1)$) with $r$ nonoverlapping success runs of length $\ge k$. We present a…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability…
Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality…
We formalize a classification of pair interactions based on the convergence properties of the {\it forces} acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF)…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
Quantile is an important measure in finance and quality assessment in service industry. In this paper, we model the temporal and cross-sectional interactive effect of the quantiles of large-dimensional time series by a latent quantile…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
Correlation functions measured as a function of $\Delta \eta, \Delta \phi$ have emerged as a powerful tool to study the dynamics of particle production in nuclear collisions at high energy. They are however subject, like any other…
Quantum mechanics predicts an exponentially small probability that a particle with energy greater than the height of a potential barrier will nevertheless reflect from the barrier in violation of classical expectations. This process can be…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We analyze the connection between $p_T$ and multiplicity distributions in a statistical framework. We connect the Tsallis parameters, $T$ and $q$, to physical properties like average energy per particle and the second scaled factorial…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…