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Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2004
We introduce and study a notion of Λ-freeness, which generalises both freeness and independence in the context of noncommutative probability. In particular, we extend Voiculescu's construction of the free product of representations of unital *-algebras. A central limit theorem is also proved.
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We introduce and study a notion of Λ-freeness, which generalises both freeness and independence in the context of noncommutative probability. In particular, we extend Voiculescu's construction of the free product of representations of unital *-algebras. A central limit theorem is also proved.
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The Lévy-Itô decomposition in free probability
Probability Theory and Related Fields, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barndorff-Nielsen, Ole Eiler +1 more
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2017
AbstractFree probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion ...
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AbstractFree probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion ...
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The Bi-free Extension of Free Probability
2016Free probability is a noncommutative probability theory adapted to variables with the highest degree of noncommutativity. The theory has connections with random matrices, combinatorics, and operator algebras. Recently, we realized that the theory has an extension to systems with left and right variables, based on a notion of bi-freeness.
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2018
The workhop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory.
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The workhop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory.
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Free probability and the von Neumann algebrasof free groups
Reports on Mathematical Physics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Conditionally Free Probability
2019That paper considers the introdution to free probability with two states. The main results are connected with quantum channels. We have proved that a free product of quantum channels – the conditionally free product of a quantum channel – is again a quantum channel.
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2009
Let us notice that by definition, a von Neumann algebra contains only bounded operators. The theory nevertheless allows us to consider unbounded operators thanks to the notion of affiliated operators. A densely defined selfadjoint operator X on H is said to be affiliated to A iff for any Borel function f on the spectrum of X, f(X) ? A (see [167, p.164])
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Let us notice that by definition, a von Neumann algebra contains only bounded operators. The theory nevertheless allows us to consider unbounded operators thanks to the notion of affiliated operators. A densely defined selfadjoint operator X on H is said to be affiliated to A iff for any Borel function f on the spectrum of X, f(X) ? A (see [167, p.164])
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Carrier-free nanomedicines for cancer treatment
Progress in Materials Science, 2022Li-Han Liu, Xian-Zheng Zhang
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