Related papers: Probability Distributions attached to generalised …
A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As…
From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…
We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
A new family of fractional counting processes based on a three-parameter generalized Mittag-Leffler function was introduced and studied. As applications we develop a fractional generalized compound process, introduce and develop fractional…
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…
In the coherent state of the harmonic oscillator, the probability density is that of the ground state subjected to an oscillation along a classical trajectory. Senitzky and others pointed out that there are states of the harmonic oscillator…
While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…
We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, $su(2)$, $su(r+1)$, $su(1,1)$ and…
We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
Linear media are predicted to exist whose relative permiability is an operator in the space of quantum states of light. Such media are characterized by a photon statistics--dependent refractive index. This indicates a new type of optical…
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for…