THE FIVE INDEPENDENCES AS NATURAL PRODUCTS

DOI10.1142/S0219025703001365zbMath1053.81057OpenAlexW2128279033MaRDI QIDQ3043507

Naofumi Muraki

Publication date: 6 August 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025703001365

zbMATH Keywords

tensor productBoolean productfree productnoncommutative probabilitymonotone productanti-monotone product

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54) Quantum stochastic calculus (81S25) Axioms; other general questions in probability (60A05)

Related Items (48)

Non-commutative stochastic independence and cumulants ⋮ Conditionally bi-free independence for pairs of faces ⋮ A note on the rate of convergence in the Boolean central limit theorem ⋮ Asymptotic Spectral Distributions of Distance-k Graphs of Star Product Graphs ⋮ Mixtures of classical and free independence ⋮ A Berry-Esseen type limit theorem for Boolean convolution ⋮ On operator-valued monotone independence ⋮ Combinatorics of NC-probability spaces with independent constants ⋮ Conditionally monotone independence II: multiplicative convolutions and infinite divisibility ⋮ Tree convolution for probability distributions with unbounded support ⋮ Generators of some non-commutative stochastic processes ⋮ The chordal Loewner equation and monotone probability theory ⋮ Cumulants, spreadability and the Campbell-Baker-Hausdorff series ⋮ Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles ⋮ Free-Boolean independence for pairs of algebras ⋮ Towards a classification of multi-faced independence: a representation-theoretic approach ⋮ On Boolean selfdecomposable distributions ⋮ Shuffle algebras and non-commutative probability for pairs of faces ⋮ Algebraic structures underlying quantum independences: theory and applications ⋮ Extended de Finetti theorems for boolean independence and monotone independence ⋮ The monotone cumulants ⋮ Traffic distributions and independence. II: Universal constructions for traffic spaces ⋮ The Bi-free Extension of Free Probability ⋮ V-monotone independence ⋮ Strict limit types for monotone convolution ⋮ Conditionally free reduced products of Hilbert spaces ⋮ CONSTRUCTIVE UNIVERSAL CENTRAL LIMIT THEOREMS BASED ON INTERACTING FOCK SPACES ⋮ QUANTUM STOCHASTIC CALCULUS ON BOOLEAN FOCK SPACE ⋮ A SIMPLE PROOF FOR MONOTONE CLT ⋮ Schoenberg correspondence on dual groups ⋮ Boolean convolutions and regular variation ⋮ Classical scale mixtures of Boolean stable laws ⋮ Loewner's differential equation and spidernets ⋮ A noncommutative de Finetti theorem for Boolean independence ⋮ Conditionally monotone independence and the associated products of graphs ⋮ Free-Boolean independence with amalgamation ⋮ Bi-monotonic independence for pairs of algebras ⋮ CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS ⋮ On a Berry-Esseen type limit theorem for Boolean convolution ⋮ Monotone cumulant-moment formula and Schröder trees ⋮ Categorial independence and Lévy processes ⋮ Classification and GNS-construction for general universal products ⋮ Monotone increment processes, classical Markov processes, and Loewner chains ⋮ An operad of non-commutative independences defined by trees ⋮ On operator-valued infinitesimal Boolean and monotone independence ⋮ On the monotone \(C^\ast \)-algebra ⋮ Some thoughts on Wilhelm von Waldenfels and on universal second order constructions ⋮ Non-commutative stochastic processes with independent increments

Cites Work

• A new example of `independence' and `white noise'
• Noncommutative Brownian motion in monotone Fock space
• White noise on bialgebras
• Direct sums of tensor products and non-commutative independence
• An algebraic version of the central limit theorem
• An algebraic central limit theorem in the anti-commuting case
• MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS
• MONOTONE INDEPENDENCE IS ASSOCIATIVE
• THE FIVE INDEPENDENCES AS QUASI-UNIVERSAL PRODUCTS
• A quantum-mechanical central limit theorem

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