UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
45.1 44.2 44.1 43.2 43.1 42.2 42.1
41.2 41.1 40.2 40.1 39.2 39.1 38.2
38.1 37.2 37.1 36.2 36.1 35.2 35.1
34.2 34.1 33.2 33.1 32.2 32.1 31.2
31.1 30.2 30.1 29.2 29.1 28.2 28.1
27.2 27.1 26.2 26.1 25.2 25.1 24.2
24.1 23.2 23.1 22.2 22.1 21.2 21.1
20.2 20.1 19.2 19.1 18.2 18.1 17.2
17.1 16.2 16.1 15 14.2 14.1 13.2
13.1 12.2 12.1 11.2 11.1 10.2 10.1
9.2 9.1 8 7.2 7.1 6.2 6.1
5.2 5.1 4.2 4.1 3.2 3.1 2.2
2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 45, Fasc. 1,
pages 101 - 114
DOI: 10.37190/0208-4147.00232
Published online 12.9.2025
 

Boolean and Fermi Central Limit Theorems

Sukrit Chakraborty

Abstract:

We provide a necessary and sufficient condition on a sequence of random variables for the Boolean and Fermi central limit theorems to hold true. The result allows us to connect the classical and the non-commutative analogues of the central limit theorems. We show that the Boolean domain of attraction of the symmetric Bernoulli distribution, the free domain of attraction of the semicircle law and the classical domain of attraction of the Gaussian distribution coincide with each other.

2010 AMS Mathematics Subject Classification: Primary 60G70; Secondary 46L53; 46L54.

Keywords and phrases: Boolean convolution, central limit theorem, regular variation.

Download:        Full text