Domain of attraction of Gaussian probability operators in quantum limit theory
Katarzyna Lubnauer, Andrzej {\L}uczak
TL;DR
This paper characterizes the class of probability operators that converge to Gaussian limits within a generalized noncommutative probability framework, extending Urbanik's classical limit theorems.
Contribution
It introduces a broader setting for noncommutative probability limit theorems and identifies the domain of attraction for Gaussian probability operators.
Findings
Characterization of probability operators in the Gaussian domain of attraction
Extension of Urbanik's limit theorem to a noncommutative setting
Generalization of classical probability limit theorems
Abstract
We characterise the class of probability operators belonging to the domain of attraction of Gaussian limits in the setup which is a slight generalisation of Urbanik's scheme of noncommutative probability limit theorems.
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Taxonomy
TopicsQuantum Mechanics and Applications