Related papers: Two-parametric fractional statistics models for an…
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
This paper presents three fractional models formulated from a classical Pharmacokinetics compartmental system: commensurable, non-commensurable, and implicit non-commensurable models. Their distinguishing characteristics are further…
The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic…
We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes…
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals, to be called "regression functionals'', defined on large…
Anyons have exotic statistical properties, fractional statistics, differing from Bosons and Fermions. They can be created as excitations of some Hamiltonian models. Here we present an experimental demonstration of anyonic fractional…
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic…
We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter $\alpha$. This alternative simpler distribution…
We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality…
The idea of fractional exclusion statistics proposed by Haldane is applied to systems with internal degrees of freedom, and its thermodynamics is examined. In case of one dimension, various bulk quantities calculated show that the critical…
Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution…
We obtain the Hausdorff dimension, $h=2-2s$, for particles with fractional spins in the interval, $0\leq s \leq 0.5$, such that the manifold is characterized by a topological invariant given by, ${\cal W}=h+2s-2p$. This object is related to…
We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a…
The fractional birth and the fractional death processes are more desirable in practice than their classical counterparts as they naturally provide greater flexibility in modeling growing and decreasing systems. In this paper, we propose…
Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…
We propose a phenomenological light-front wave function for hadrons with arbitrary twist-dimension (mesons, baryons and multiquark states), which gives the correct scaling behavior of structure functions (parton distributions) and form…