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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Certain group dynamical systems induced by Hecke algebras [PDF]
Opuscula Mathematica, 2016 In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number ...
Ilwoo Cho
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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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Deformation of semicircular and circular laws via p-adic number fields and sampling of primes [PDF]
Opuscula Mathematica, 2019 In this paper, we study semicircular elements and circular elements in a certain Banach \(*\)-probability space \((\mathfrak{LS},\tau ^{0})\) induced by analysis on the \(p\)-adic number fields \(\mathbb{Q}_{p}\) over primes \(p\).
Ilwoo Cho, Palle E. T. Jorgensen
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Banach-Space Operators Acting on Semicircular Elements Induced by p-Adic Number Fields over Primes p
Mathematics, 2019 In this paper, we study certain Banach-space operators acting on the Banach *-probability space ( LS , τ 0 ) generated by semicircular elements Θ p , j induced by p-adic number fields Q p over the set P of all
Ilwoo Cho
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Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras
Mathematics, 2017 In this paper, we construct a free semicircular family induced by Z -many mutually-orthogonal projections, and construct Banach ∗-probability spaces ...
Ilwoo Cho
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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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Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields
Mathematics, 2019 In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p .
Ilwoo Cho, Palle Jorgensen
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Free probability induced by electric resistance networks on energy Hilbert spaces [PDF]
Opuscula Mathematica, 2011 We show that a class of countable weighted graphs arising in the study of electric resistance networks (ERNs) are naturally associated with groupoids.
Ilwoo Cho, Palle E. T. Jorgensen
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Operation State Evaluation Method of Smart Distribution Network Based on Free Probability Theory
Frontiers in Energy Research, 2022 In view of the current situation that the new generation of smart grids with “double high” characteristics is in urgent need of effective state evaluation methods due to the characteristics of strong volatility and diverse demands, a method of operation ...
Jiaxin Zhang +6 more
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