51 citations · 164 across the 12 of their papers we have counts for
6 papers · 1 filter
Limit distribution in the -CLT for can not have a compact support
Sabir Umarov, Constantino Tsallis
In a recent paper Hilhorst \cite{Hilhorst2010} illustrated that the -Fourier transform for is not invertible in the space of density functions. Using an invariance princip…
On a representation of the inverse Fq transform
Sabir Umarov, Constantino Tsallis
A recent generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted $q…
Multivariate Generalizations of the q--Central Limit Theorem
Sabir Umarov, Constantino Tsallis
We study multivariate generalizations of the -central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics.…
Symmetric -Stable Distributions. Part II: Second Representation
Sabir Umarov, Constantino Tsallis, Murray Gell-Mann +1
This paper is a continuation of papers \cite{UmarovTsallisSteinberg,UmarovTsallisGellmannSteinberg}. In Part I \cite{UmarovTsallisGellmannSteinberg} a description (representation)…
Symmetric -Stable Distributions. Part I: First Representation
Sabir Umarov, Constantino Tsallis, Murray Gell-Mann +1
The classic central limit theorem and -stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the…
A generalization of the central limit theorem consistent with nonextensive statistical mechanics
Sabir Umarov, Constantino Tsallis, Stanly Steinberg
The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988…