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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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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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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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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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From Type-Free Truth to Type-Free Probability
2012One way of stating Tarski’s classical limitative result on truth informally is that one cannot accept all T-biconditionals for a semantically closed language LTr that includes a type-free truth predicate Tr.
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Free Energies of Proton-Coupled Electron Transfer Reagents and Their Applications
Chemical Reviews, 2022Rishi G Agarwal +2 more
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Theory of Nonequilibrium Free Energy Transduction by Molecular Machines
Chemical Reviews, 2020Aidan I Brown, David A Sivak
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Methylammonium-free wide-bandgap metal halide perovskites for tandem photovoltaics
Nature Reviews Materials, 2023Alexandra J Ramadan +2 more
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