Limit Measures Related to the Conditionally Free Convolution

Melanie Hinz; Wojciech Młotkowski

Displaying similar documents to “Limit Measures Related to the Conditionally Free Convolution”

On some generalization of the t-transformation

Anna Dorota Krystek (2010)

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Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation $U^{}$ of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the...

Radial Convolutors on Free Groups

T. Pytlik (1982)

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Operator-valued version of conditionally free product

Wojciech Młotkowski (2002)

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We present an operator-valued version of the conditionally free product of states and measures, which in the scalar case was studied by Bożejko, Leinert and Speicher. The related combinatorics and limit theorems are provided.

New Examples of Convolutions and Non-Commutative Central Limit Theorems

Marek Bożejko, Janusz Wysoczański (1998)

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A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.

Decomposability of point measures in generalized convolution algebras

J. Kucharczak (1988)

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On convolution products of radial measures on the Heisenberg group

Krzysztof Stempak (1985)

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A remark on p-convolution

Rafał Sałapata (2011)

Banach Center Publications

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We introduce a p-product of algebraic probability spaces, which is the definition of independence that is natural for the model of noncommutative Brownian motions, described in [10] (for q = 1). Using methods of the conditionally free probability (cf. [4, 5]), we define a related p-convolution of probability measures on ℝ and study its relations with the notion of subordination (cf. [1, 8, 9, 13]).

Asymptotic formulae concerning arithmetical functions defined by cross-convolutions. VI: $A$ - $k$ -free integers.

Tóth, László (1997)

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Measures and Convolution Products with Small Transforms.

Louis Pigno (1971)

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Convolutions related to q-deformed commutativity

Anna Kula (2010)

Banach Center Publications

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Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution...

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E. Gesztelyi (1970)

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The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution

Łukasz Jan Wojakowski (2007)

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We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by $μ ⊞_{T} ν = T^{- 1} (T μ ⊞ T ν)$ . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution...

On a convolution type integral I

S. R. Yadava (1972)

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Semigroups related to additive and multiplicative, free and Boolean convolutions

Octavio Arizmendi, Takahiro Hasebe (2013)

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Belinschi and Nica introduced a composition semigroup of maps on the set of probability measures. Using this semigroup, they introduced a free divisibility indicator, from which one can know quantitatively if a measure is freely infinitely divisible or not. In the first half of the paper, we further investigate this indicator: we calculate how the indicator changes with respect to free and Boolean powers; we prove that free and Boolean 1/2-stable laws have free divisibility indicators...

Convolution in Colombeau's spaces of generalized functions. II: The convolution in $𝒢_{a}$ .

Nedeljkov, M., Pilipović, S. (1992)

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The Neutrix Convolution Product x -r,- ○ x μ,+

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Probability measures corresponding to Aval numbers

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We describe the class of probability measures whose moments are given in terms of the Aval numbers. They are expressed as the multiplicative free convolution of measures corresponding to the ballot numbers $(m - k) / (m + k) (\binom{m + k}{m})$ .

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Kazimierz Urbanik (1967)

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A note on the convolution in the Mellin sense with generalized functions.

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The number of (2,3)-sum-free subsets of {1,...,n}

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Uwe Franz (2006)

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Recently, Bercovici has introduced multiplicative convolutions based on Muraki's monotone independence and shown that these convolution of probability measures correspond to the composition of some function of their Cauchy transforms. We provide a new proof of this fact based on the combinatorics of moments. We also give a new characterisation of the probability measures that can be embedded into continuous monotone convolution semigroups of probability measures on the unit circle and...