MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS

DOI10.1142/S0219025701000334zbMath1046.46049MaRDI QIDQ4460437

Publication date: 18 May 2004

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

Mathematics Subject Classification ID

Noncommutative probability and statistics (46L53) Probability theory on algebraic and topological structures (60B99) Limit theorems in probability theory (60F99)

Related Items (70)

Non-commutative stochastic independence and cumulants ⋮ From discrete to continuous monotone C*-algebras via quantum central limit theorems ⋮ Relations between convolutions and transforms in operator-valued free probability ⋮ Asymptotic Spectral Distributions of Distance-k Graphs of Star Product Graphs ⋮ Discrete Löwner evolution. ⋮ Meixner class of orthogonal polynomials of a non-commutative monotone Lévy noise ⋮ Wick polynomials in noncommutative probability: a group-theoretical approach ⋮ ROTATION INVARIANT INTERACTING FOCK SPACES ⋮ A Berry-Esseen type limit theorem for Boolean convolution ⋮ REDUCTION OF FREE INDEPENDENCE TO TENSOR INDEPENDENCE ⋮ MONOTONE INDEPENDENCE, COMB GRAPHS AND BOSE–EINSTEIN CONDENSATION ⋮ LIMIT THEOREMS IN Λ-BOOLEAN PROBABILITY ⋮ Combinatorics of NC-probability spaces with independent constants ⋮ Conditionally monotone independence II: multiplicative convolutions and infinite divisibility ⋮ Maximal inequalities in noncommutative probability spaces ⋮ Tree convolution for probability distributions with unbounded support ⋮ On monotone product of operator algebras ⋮ Decompositions of the free additive convolution ⋮ Limits of some weighted Cesaro averages ⋮ Cumulants, spreadability and the Campbell-Baker-Hausdorff series ⋮ Distribution for non symmetric position operators on the free toy Fock space and its approximation on the full Fock space ⋮ DECOMPOSITIONS OF THE FREE PRODUCT OF GRAPHS ⋮ Spectra of infinite graphs via freeness with amalgamation ⋮ Towards a classification of multi-faced independence: a representation-theoretic approach ⋮ The monotone cumulants ⋮ BM-CENTRAL LIMIT THEOREMS FOR POSITIVE DEFINITE REAL SYMMETRIC MATRICES ⋮ On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws ⋮ Asymptotic properties of random matrices and pseudomatrices ⋮ V-monotone independence ⋮ Monotone quantum stochastic processes and covariant dynamical hemigroups ⋮ Free probability for pairs of faces. I ⋮ Strict limit types for monotone convolution ⋮ Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection ⋮ Some relatives of the Catalan sequence ⋮ FOURIER AND CAUCHY–STIELTJES TRANSFORMS OF POWER LAWS INCLUDING STABLE DISTRIBUTIONS ⋮ NONCOMMUTATIVE BROWNIAN MOTIONS ASSOCIATED WITH KESTEN DISTRIBUTIONS AND RELATED POISSON PROCESSES ⋮ Conditionally free reduced products of Hilbert spaces ⋮ Unimodality of Boolean and monotone stable distributions ⋮ Distributions for nonsymmetric monotone and weakly monotone position operators ⋮ A NEW LOOK AT THE ARCSINE LAW AND "QUANTUM-CLASSICAL CORRESPONDENCE" ⋮ MONOTONE CONVOLUTION AND MONOTONE INFINITE DIVISIBILITY FROM COMPLEX ANALYTIC VIEWPOINT ⋮ Wick order, spreadability and exchangeability for monotone commutation relations ⋮ Probability distributions with binomial moments ⋮ A SIMPLE PROOF FOR MONOTONE CLT ⋮ Matricially free random variables ⋮ A REMARK ON MONOTONIC CONVOLUTION ⋮ THE FIVE INDEPENDENCES AS NATURAL PRODUCTS ⋮ Schoenberg correspondence on dual groups ⋮ bm-INDEPENDENCE AND bm-CENTRAL LIMIT THEOREMS ASSOCIATED WITH SYMMETRIC CONES ⋮ Loewner's differential equation and spidernets ⋮ On the class of distributions of subordinated Lévy processes and bases ⋮ On the path structure of a semimartingale arising from monotone probability theory ⋮ NONCOMMUTATIVE BROWNIAN MOTIONS INDEXED BY PARTIALLY ORDERED SETS ⋮ Relations between cumulants in noncommutative probability ⋮ Conditionally monotone independence and the associated products of graphs ⋮ MONOTONIC INDEPENDENCE ON THE WEAKLY MONOTONE FOCK SPACE AND RELATED POISSON TYPE THEOREM ⋮ Weakly monotone Fock space and monotone convolution of the Wigner law ⋮ Bi-monotonic independence for pairs of algebras ⋮ DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY ⋮ Operator-valued chordal Loewner chains and non-commutative probability ⋮ bm-Central Limit Theorems associated with non-symmetric positive cones ⋮ Unnamed Item ⋮ Joint monotone and Boolean numerical and spectral radii of \(d\)-tuples of operators ⋮ The qq-bit (I): Central limits with left q-Jordan–Wigner embeddings, monotone interacting Fock space, Azema random variable, probabilistic meaning of q ⋮ Quantum Lévy processes on dual groups ⋮ Monotone increment processes, classical Markov processes, and Loewner chains ⋮ An operad of non-commutative independences defined by trees ⋮ MONOTONIC INDEPENDENCE ASSOCIATED WITH PARTIALLY ORDERED SETS ⋮ On the monotone \(C^\ast \)-algebra ⋮ Motzkin path decompositions of functionals in noncommutative probability

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