Note on aq-modified central limit theorem

DOI10.1088/1742-5468/2010/10/P10023zbMath1456.60060arXiv1008.4259OpenAlexW3105255942WikidataQ63214553 ScholiaQ63214553MaRDI QIDQ3301136

Hendrik Jan Hilhorst

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4259

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) General theory of stochastic processes (60G07) Foundations of equilibrium statistical mechanics (82B03)

Related Items (11)

Towards a large deviation theory for strongly correlated systems ⋮ \(\kappa\)-deformed Fourier transform ⋮ Extension of inverse \(q\)-Fourier transform via conformal mapping ⋮ Reflections on the \(q\)-Fourier transform and the \(q\)-Gaussian function ⋮ \(q\)-generalized representation of the \(d\)-dimensional Dirac delta and \(q\)-Fourier transform ⋮ The confidence interval of q-Gaussian distributions ⋮ \(q\)-generalization of the inverse Fourier transform ⋮ The transformation groupoid structure of the \(q\)-Gaussian family ⋮ Connection between Dirichlet distributions and a scale-invariant probabilistic model based on Leibniz-like pyramids ⋮ Approach of complexity in nature: entropic nonuniqueness ⋮ Influence of the interaction range on the thermostatistics of a classical many-body system

Cites Work

• Unnamed Item
• On a representation of the inverse \(F_{q}\)-transform
• Nonextensive statistical mechanics, anomalous diffusion and central limit theorems
• On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
• Possible generalization of Boltzmann-Gibbs statistics.
• Introduction to Nonextensive Statistical Mechanics
• On multivariate generalizations of the q-central limit theorem consistent with nonextensive statistical mechanics
• Escort mean values and the characterization of power-law-decaying probability densities
• A note onq-Gaussians and non-Gaussians in statistical mechanics
• Generalization of symmetric α-stable Lévy distributions for q>1
• New representations of π and Dirac delta using the nonextensive-statistical-mechanics q-exponential function
• Functional differential equations for theq-Fourier transform ofq-Gaussians

This page was built for publication: Note on aq-modified central limit theorem