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Physical Review X, 2023 Unitary designs have become a vital tool for investigating pseudorandomness, since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relations to quantum chaotic evolution and, in ...
Michele Fava +2 more
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Free probability for probabilists [PDF]
, 1998 This is an introduction to some of the most probabilistic aspects of free probability ...
Biane, Philippe
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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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Limit theorems in free probability theory II [PDF]
Open Mathematics, 2008 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.
Chistyakov Gennadii, Götze Friedrich
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Phase-probability shaping for speckle-free holographic lithography [PDF]
Nature CommunicationsOptical holography has undergone rapid development since its invention in 1948, but the accompanying speckles with alternating dark and bright spots of randomly varying shapes are still untamed now due to the intrinsic fluctuations from irregular complex-
Dong Zhao +5 more
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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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