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The arithmetic of distributions in free probability theory [PDF]
Open Mathematics, 2011 Abstract We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the ...
Chistyakov Gennadii, Götze Friedrich
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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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Banach *-algebras generated by semicircular elements induced by certain orthogonal projections [PDF]
Opuscula Mathematica, 2018 The main purpose of this paper is to study structure theorems of Banach \(*\)-algebras generated by semicircular elements. In particular, we are interested in the cases where given semicircular elements are induced by orthogonal projections in a \(C^{*}\)
Ilwoo Cho, Palle E. T. Jorgensen
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IEEE Access, 2021 In this paper, we investigate channel estimation and robust detection for uplink massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with in-phase and quadrature-phase imbalances (IQI).
Yan Chen +4 more
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Semicircular elements induced by p-adic number fields [PDF]
Opuscula Mathematica, 2017 In this paper, we study semicircular-like elements, and semicircular elements induced by \(p\)-adic analysis, for each prime \(p\). Starting from a \(p\)-adic number field \(\mathbb{Q}_{p}\), we construct a Banach \(*\)-algebra \(\mathfrak{LS}_{p}\), for
Ilwoo Cho, Palle E. T. Jorgensen
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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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Universal probability-free prediction [PDF]
Annals of Mathematics and Artificial Intelligence, 2017 27 ...
Vladimir Vovk, Dusko Pavlovic
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Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras [PDF]
Opuscula Mathematica, 2016 In this paper, by establishing free-probabilistic models on the Hecke algebras \(\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)\) induced by \(p\)-adic number fields \(\mathbb{Q}_{p}\), we construct free probability spaces for all primes \(p\).
Ilwoo Cho
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Hopf algebras and the logarithm of the S-transform in free probability ― Extended abstract [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 This document is an extended abstract of the paper `Hopf algebras and the logarithm of the S-transform in free probability' in which we introduce a Hopf algebraic approach to the study of the operation $\boxtimes$ (free multiplicative convolution) from ...
Mitja Mastnak, Alexandru Nica
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