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Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic…
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…
The probability distribution function for thermodynamics and econophysics is obtained by solving an equilibrium equation. This approach is different from the common one of optimizing the entropy of the system or obtaining the state of…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability…
This article reviews the concepts and methods of variational path sampling. These methods allow computational studies of rare events in systems driven arbitrarily far from equilibrium. Based upon a statistical mechanics of trajectory space…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
Anomalous transport in tilted periodic potentials is investigated within the framework of the fractional Fokker-Planck dynamics and the underlying continuous time random walk. The analytical solution for the stationary, anomalous current is…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a…
We discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
We consider a multi-type branching random walk with displacements that have either regularly varying or semi-exponential tails. We investigate the asymptotic behavior of the rightmost particle in irreducible and reducible regimes and…
This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general…
The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
Very recently we present a theory to discuss the nature of light and show that the quantization of light energy in vacuum can be derived directly from classical electromagnetic theory. In the theory a key concept of stability of statistical…