Cumulants in noncommutative probability theory II
نویسندگان
چکیده
منابع مشابه
Cumulants in Noncommutative Probability Theory I. Noncommutative Exchangeability Systems
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting. It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the formula says that cumulants are moments of a certain “discrete Fourier transform” of a random variable. This provides a simple unified method to understand ...
متن کاملRelations between Cumulants in Noncommutative Probability
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed.
متن کاملCumulants in Noncommutative Probability Theory Iv. Noncrossing Cumulants: De Finetti’s Theorem, L-inequalities and Brillinger’s Formula
In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. De Finetti’s theorem states that any exchangeable sequence of random variables is conditionally i.i.d. with respect to some σ-algebra. In this paper we prove a “free” noncommutative analog of this theorem, namely we show that any noncrossing...
متن کاملCumulants in Noncommutative Probability Theory III. Creation and annihilation operators on Fock spaces
Cumulants of noncommutative random variables arising from Fock space constructions are considered. In particular, simplified calculations are given for several known examples on q-Fock spaces. In the second half of the paper we consider in detail the Fock states associated to characters of the infinite symmetric group recently constructed by Bożejko and Guta. We express moments of multidimensio...
متن کاملCumulants of a convolution and applications to monotone probability theory
In non-commutative probability theory, cumulants and their appropriate generating function are defined when a notion of independence is given [17, 18, 19]. They are useful especially in the central limit theorem and Poisson’s law of small numbers. We denote by any one of classical, free and boolean convolutions. We denote by Dλ the dilation operator defined by (Dλμ)(B) = μ(λ B) for any Borel se...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2003
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-003-0292-0