Unification of Independence in Quantum Probability

DOI10.1142/S021902579800020XzbMath0928.46044arXivmath/0103031MaRDI QIDQ4236737

Romuald Lenczewski

Publication date: 28 March 1999

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

Full work available at URL: https://arxiv.org/abs/math/0103031

zbMATH Keywords

noncommutative independenceBoolean extensionsfree *-algebrastensor independence*-bialgebrasconditionally free product state on word productsunital *-homomorphisms

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Quantum stochastic calculus (81S25)

Related Items (18)

THE FIVE INDEPENDENCES AS QUASI-UNIVERSAL PRODUCTS ⋮ REDUCTION OF FREE INDEPENDENCE TO TENSOR INDEPENDENCE ⋮ MONOTONE INDEPENDENCE, COMB GRAPHS AND BOSE–EINSTEIN CONDENSATION ⋮ Tree convolution for probability distributions with unbounded support ⋮ Decompositions of the free additive convolution ⋮ Fermions from classical probability and statistics defined by stochastic independence ⋮ DECOMPOSITIONS OF THE FREE PRODUCT OF GRAPHS ⋮ V-monotone independence ⋮ Remarks on the \(r\) and \(\Delta\) convolutions ⋮ Filtered random variables, bialgebras, and convolutions ⋮ Appell polynomials and their relatives. III: Conditionally free theory ⋮ Conditionally monotone independence and the associated products of graphs ⋮ MONOTONIC INDEPENDENCE ON THE WEAKLY MONOTONE FOCK SPACE AND RELATED POISSON TYPE THEOREM ⋮ DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY ⋮ FILTERED STOCHASTIC CALCULUS ⋮ An information complexity index for probability measures on ℝ with all moments ⋮ Unnamed Item ⋮ Motzkin path decompositions of functionals in noncommutative probability

Cites Work

• Convolution and limit theorems for conditionally free random variables
• On sums of \(q\)-independent \(\text{SU}_ q(2)\) quantum variables
• An algebraic version of the central limit theorem
• ADDITION OF INDEPENDENT VARIABLES IN QUANTUM GROUPS
• A quantum-mechanical central limit theorem

This page was built for publication: Unification of Independence in Quantum Probability