Convolution and limit theorems for conditionally free random variables
From MaRDI portal
Publication:1359200
DOI10.2140/pjm.1996.175.357zbMath0874.60010arXivfunct-an/9410004OpenAlexW1532235125MaRDI QIDQ1359200
Roland Speicher, Marek Bożejko, Michael Leinert
Publication date: 10 November 1997
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/funct-an/9410004
Stochastic analysis (60H99) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)
Related Items (86)
Non-commutative stochastic independence and cumulants ⋮ Conditionally bi-free independence for pairs of faces ⋮ Δ-Cumulants in terms of moments ⋮ Analytic subordination for bi-free convolution ⋮ Wick polynomials in noncommutative probability: a group-theoretical approach ⋮ BI-POISSON PROCESS ⋮ On the Matsumoto-Yor property in free probability ⋮ Cumulants in noncommutative probability theory. IV: Noncrossing cumulants: de Finetti's theorem and \(L^{p}\)-inequalities ⋮ THE FIVE INDEPENDENCES AS QUASI-UNIVERSAL PRODUCTS ⋮ FERMI CONVOLUTION ⋮ New characterization of two-state normal distribution ⋮ Dual Lukacs regressions of negative orders for noncommutative variables ⋮ LIMIT THEOREMS IN Λ-BOOLEAN PROBABILITY ⋮ A QUADRATIC REGRESSION PROBLEM FOR TWO-STATE ALGEBRAS WITH AN APPLICATION TO THE CENTRAL LIMIT THEOREM ⋮ COMBINATORIAL RELATION BETWEEN FREE CUMULANTS AND JACOBI PARAMETERS ⋮ Combinatorics of NC-probability spaces with independent constants ⋮ Conditionally monotone independence II: multiplicative convolutions and infinite divisibility ⋮ Asymptotic expansions in the CLT in free probability ⋮ Tree convolution for probability distributions with unbounded support ⋮ Two-state free Brownian motions ⋮ Generators of some non-commutative stochastic processes ⋮ Decompositions of the free additive convolution ⋮ Semigroups of distributions with linear Jacobi parameters ⋮ Cumulants, spreadability and the Campbell-Baker-Hausdorff series ⋮ Towards a classification of multi-faced independence: a representation-theoretic approach ⋮ The double Fock space of type B ⋮ Unitary dilation of freely independent contractions ⋮ Cyclic independence: Boolean and monotone ⋮ Quantum holonomy fields ⋮ Meixner class of non-commutative generalized stochastic processes with freely independent values. II: The generating function ⋮ Cumulants, lattice paths, and orthogonal polynomials ⋮ On truncated \(t\)-free Fock spaces: spectrum of position operators and shift-invariant states ⋮ V-monotone independence ⋮ Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection ⋮ Characterizations of some free random variables by properties of conditional moments of third degree polynomials ⋮ INFINITE DIVISIBILITY FOR THE CONDITIONALLY FREE CONVOLUTION ⋮ Dual Lukacs regressions for non-commutative variables ⋮ An alternating moment condition for bi-freeness ⋮ BESSIS–MOUSSA–VILLANI CONJECTURE AND GENERALIZED GAUSSIAN RANDOM VARIABLES ⋮ NONCOMMUTATIVE BROWNIAN MOTIONS ASSOCIATED WITH KESTEN DISTRIBUTIONS AND RELATED POISSON PROCESSES ⋮ Conditionally free reduced products of Hilbert spaces ⋮ Spectral theory of Fourier-Stieltjes algebras ⋮ Matricial \(R\)-transform ⋮ Non-crossing linked partitions, the partial order ≪ on 𝑁𝐶(𝑛), and the 𝑆-transform ⋮ THE NUMBER OF PURE CONVOLUTIONS ARISING FROM CONDITIONALLY FREE CONVOLUTION ⋮ ASSOCIATIVE CONVOLUTIONS ARISING FROM CONDITIONALLY FREE CONVOLUTION ⋮ Distributions for nonsymmetric monotone and weakly monotone position operators ⋮ Free Meixner states ⋮ Graph products of operator algebras ⋮ A Fock space model for addition and multiplication of c-free random variables ⋮ Bi-Boolean independence for pairs of algebras ⋮ The von Neumann algebras generated by \(t\)-Gaussians ⋮ Remarks on the \(r\) and \(\Delta\) convolutions ⋮ Appell polynomials and their relatives. III: Conditionally free theory ⋮ On a class of free Lévy laws related to a regression problem ⋮ Conditional moments of \(q\)-Meixner processes ⋮ NONCOMMUTATIVE BROWNIAN MOTIONS INDEXED BY PARTIALLY ORDERED SETS ⋮ Free-Boolean independence with amalgamation ⋮ Bi-monotonic independence for pairs of algebras ⋮ DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY ⋮ On Lehner’s ‘free’ noncommutative analogue of de Finetti’s theorem ⋮ MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS ⋮ QUANTUM DECOMPOSITION IN DISCRETE GROUPS AND INTERACTING FOCK SPACES ⋮ CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS ⋮ Multi-variable subordination distributions for free additive convolution ⋮ THE COMBINATORICS OF THE r-FREE CONVOLUTION ⋮ On multiplicative conditionally free convolution ⋮ Λ-FREE PROBABILITY ⋮ INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES ⋮ A group-theoretical approach to conditionally free cumulants ⋮ Unnamed Item ⋮ A construction which relates $c$-freeness to infinitesimal freeness ⋮ Notions of Independence Related to the Free Group ⋮ Conditionally free semi-stable distributions ⋮ Categorial independence and Lévy processes ⋮ Classification and GNS-construction for general universal products ⋮ Brown's spectral distribution measure for \(R\)-diagonal elements in finite von Neumann algebras ⋮ ON STOCHASTIC DOMINANCE OF NILPOTENT OPERATORS ⋮ An operad of non-commutative independences defined by trees ⋮ Free stochastic measures via noncrossing partitions ⋮ Regression conditions that characterize free-Poisson and free-Kummer distributions ⋮ Continuous unital dilations of completely positive semigroups ⋮ Interacting Fock Spaces and Gaussianization of Probability Measures ⋮ Unification of Independence in Quantum Probability ⋮ Multinomial identities arising from free probability theory. ⋮ Algebraic central limit theorems: A personal view on one of Wilhelm’s legacies
This page was built for publication: Convolution and limit theorems for conditionally free random variables
