A dimension scale-invariant probabilistic model based on Leibniz-like pyramids

DOI10.1063/1.3688312zbMath1274.82024arXiv1107.1108OpenAlexW3099283762WikidataQ123012912 ScholiaQ123012912MaRDI QIDQ2861692

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Publication date: 11 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.1108

zbMATH Keywords

\(q\)-statistics

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Statistical thermodynamics (82B30) Irreversible thermodynamics, including Onsager-Machlup theory (82C35) Irreversible thermodynamics, including Onsager-Machlup theory (82B35)

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Stochastic dynamics of \(N\) correlated binary variables and non-extensive statistical mechanics, Groups, nonadditive entropy and phase transitions, Entropic extensivity and large deviations in the presence of strong correlations, Connection between Dirichlet distributions and a scale-invariant probabilistic model based on Leibniz-like pyramids, Generating functions for generalized binomial distributions, On the robustness of the \(q\)-Gaussian family, Emergence of q-statistical functions in a generalized binomial distribution with strong correlations

Cites Work

• Scale invariance and related properties of \(q\)-Gaussian systems
• 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
• Generalization of symmetric α-stable Lévy distributions for q>1