Related papers: About an alternative distribution function for fra…
We show that the thermodynamics of $N$ identical fermions maps onto that of distinguishable particles governed by a collective statistical potential -- the microscopic origin of degeneracy pressure. Known to be purely repulsive for ${N=2}$,…
The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…
Recent analyses of the field enhancement factor (FEF) from multiple emitters have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown…
It has long been established that, if a panel dataset suffers from attrition, auxiliary (refreshment) sampling restores full identification under additional assumptions that still allow for nontrivial attrition mechanisms. Such…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and colored permutations. The corresponding…
In this paper, we define a fractional negative binomial process (FNBP) by replacing the Poisson process by a fractional Poisson process (FPP) in the gamma subordinated form of the negative binomial process. First, it is shown that the…
By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter $\xi$…
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970's, and only proved very recently, that there is a multitude of further constraints on these…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
A useful tool in non perturbative studies of fermionic theories is partial bosonization. However, partial bosonization is often connected to an ambiguity due to Fierz rearrangement in the original theory. We discuss two different…
Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities…
The fractional Poisson process (FPP) generalizes the standard Poisson process by replacing exponentially distributed return times with Mittag-Leffler distributed ones with an extra tail parameter, allowing for greater flexibility. The FPP…
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…
In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where…
We consider two fractional versions of a family of nonnegative integer valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As…
The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of…