The law of large numbers for free identically distributed random variables

DOI10.1214/aop/1042644726zbMath0862.46036OpenAlexW2079521445MaRDI QIDQ1922088

Vittorino Pata, Hari Bercovici

Publication date: 25 May 1997

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1042644726

zbMATH Keywords

distributionfree convolutionweak law of large numbersfree identically distributed random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (10)

Inequalities for martingales with respect to positive module operators ⋮ Free subexponentiality ⋮ Unnamed Item ⋮ On superconvergence of sums of free random variables ⋮ Limit theorems in free probability theory. I ⋮ The strong laws of large numbers for positive measurable operators and applications ⋮ Convergence rates for weighted sums in noncommutative probability space ⋮ Noncommutative Baum--Katz theorems ⋮ Functions of regular variation and freely stable laws ⋮ Series of free random variables

Cites Work

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• Addition of certain non-commuting random variables
• Addition of freely independent random variables
• Some weak laws of large numbers in noncommutative probability
• A one-parameter family of transforms, linearizing convolution laws for probability distributions
• Operator algebras and their connections with topology and ergodic theory. Proceedings of the OATE Conference held in Buşteni, Romania, August 29 - September 9, 1983. With the assistance of Gr. Arsene

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