DOMAIN OF ATTRACTION OF GAUSSIAN PROBABILITY OPERATORS
IN QUANTUM LIMIT THEORY
Katarzyna Lubnauer
Andrzej Łuczak
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.
2000 AMS Mathematics Subject Classification: Primary: 46L53; Secondary:
28D05.
Keywords and phrases: Probability operators, quantum limit theorem, domain of
attraction.