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Limit Theorems in Free Probability Theory I [PDF]
Open Mathematics, 2006 Abstract Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle $$ \mathbb{T} $$ we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
G. P. Chistyakov, Friedrich Götze
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Conditional catheter-related thrombosis free probability and risk-adapted choices of catheter for lung cancer. [PDF]
Thorac Cancer, 2022 Wang Y +8 more
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Lévy laws in free probability [PDF]
Proceedings of the National Academy of Sciences, 2002 This article and its sequel outline recent developments in the theory of infinite divisibility and Lévy processes in free probability, a subject area belonging to noncommutative (or quantum) probability. The present paper discusses the classes of infinitely divisible probability measures in classical and free probability, respectively, via a study of ...
Barndorff-Nielsen, O.E. +1 more
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Lévy processes in free probability [PDF]
Proceedings of the National Academy of Sciences, 2002 This is the continuation of a previous article that studied the relationship between the classes of infinitely divisible probability measures in classical and free probability, respectively, via the Bercovici–Pata bijection. Drawing on the results of the preceding article, the present paper outlines recent developments in the theory of Lévy processes ...
Barndorff-Nielsen, O.E. +1 more
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Sums of commutators in free probability [PDF]
Journal of Functional Analysis, 2021 We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of odd cumulants * symmetric distribution for any free family.
Wiktor Ejsmont, Franz Lehner
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DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006 We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki in monotone probability and the free product of states of Avitzour and Voiculescu in free probability.
Lenczewski, Romuald, Sałapata, Rafał
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Universal probability-free prediction [PDF]
Annals of Mathematics and Artificial Intelligence, 2017 27 ...
Vladimir Vovk, Dusko Pavlovic
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FREE PROBABILITY FOR PROBABILISTS [PDF]
, 2010 This is an introduction to some of the most probabilistic aspects of free probability theory.
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Matrix concentration inequalities and free probability
Inventiones mathematicae, 2023 56 ...
Bandeira, Afonso S. +2 more
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, 2015 This article focuses on free probability theory, which is useful for dealing with asymptotic eigenvalue distributions in situations involving several matrices. In particular, it considers some of the basic ideas and results of free probability theory, mostly from the random matrix perspective.
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