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We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of…
The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the…
We present a molecular dynamics simulation study of the liquid-solid transition in a two dimensional system consisting of particles of two different sizes interacting via a truncated Lennard-Jones potential. We work with equal number of…
We investigate a zero-range process where the underlying one-particle stationary distribution has multifractality. The multiparticle stationary probability measure can be written in a factorized form. If the number of the particles is…
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
The probability distribution functions of the circulation of velocity in three-dimensional decaying isotropic turbulence are examined by the database of the numerical simulation based on the pseudospectral method. It is shown that the…
In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so…
Quantum field model of unstable particles with random mass is suggested to describe the finite-width effects in decay rate. Within the framework of this model we derive the convolution formula for a width of the channels with unstable…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We present an extensive but concise review of our present understanding, largely based on theory and simulation work from our group, on the equilibrium behavior of solid surfaces and nanosystems close to the bulk melting point. In the first…
The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
We consider the 1D motion of an overdamped Brownian particle in a general potential in the low temperature limit. We derive an explicit expression for the probability distribution for the heat transferred to the particle. We find that the…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…