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In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces.
An approach to the theory of pressure broadening of spectral lines
Wilhelm von Waldenfels · 1973
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Quantum Ito’s formula and stochastic evolutions
R. L. Hudson and K. R. Parthasarathy · 1984
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Symmetries of some reduced free product C ∗ C^{\ast} -algebras
Dan-Virgil Voiculescu · 1985
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Dual algebraic structures on operator algebras related to free products
Dan-Virgil Voiculescu · 1987
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A new example of “independence” and “white noise”
Roland Speicher · 1990
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ψ \psi -independent and symmetrized white noises
Marek Bożejko and Roland Speicher · 1991
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Convolution and limit theorems for conditionally free random variables
Marek Bożejko, Michael Leinert, and Roland Speicher · 1996
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An interacting free Fock space and the arcsine law
Y. G. Lu · 1997
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Noncommutative Brownian motion in monotone Fock space
Naofumi Muraki · 1997
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On universal products
Roland Speicher · 1997
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Categories for the working mathematician
Saunders Mc Lane · 1998
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Hopf algebras
Sorin Dăscălescu, Constantin Năstăsescu, and Şerban Raianu · 2001
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Monotonic independence, monotonic central limit theorem and monotonic law of small numbers
Naofumi Muraki · 2001
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Non-commutative notions of stochastic independence
Anis Ben Ghorbal and Michael Schürmann · 2002
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The five independences as quasi-universal products
Naofumi Muraki · 2002
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The five independences as natural products
Naofumi Muraki · 2003
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Quantum Lévy processes on dual groups
Anis Ben Ghorbal and Michael Schürmann · 2005
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Lévy processes on quantum groups and dual groups
Conditionally monotone independence I: Independence, additive convolutions and related convolutions
Takahiro Hasebe · 2011
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The monotone cumulants
Takahiro Hasebe and Hayato Saigo · 2011
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A simple proof of the classification theorem for positive natural products
Naofumi Muraki · 2013
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On several problems in the theory of comonoidal systems and subproduct systems
Malte Gerhold · 2014
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Schoenberg correspondence on dual groups
Michael Schürmann and Stefan Voß · 2014
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Free probability for pairs of faces I
Dan-Virgil Voiculescu · 2014
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Uwe Franz · 2006
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Hopf algebras in renormalisation
Dominique Manchon · 2008
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Monoidal functors, species and Hopf algebras
Marcelo Aguiar and Swapneel Mahajan · 2010
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Two-state free Brownian motions
Michael Anshelevich · 2011
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Relations between cumulants in noncommutative probability
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner, and Carlos Vargas · 2015
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Homogeneous Lie groups and quantum probability
Roland Friedrich and John McKay · 2015
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Classification and GNS-construction for general universal products
Malte Gerhold and Stephanie Lachs · 2015
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A new family of universal products and aspects of a non-positive quantum probability theory
Stephanie Lachs · 2015
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