The search session has expired. Please query the service again.

Displaying similar documents to “Semigroups related to additive and multiplicative, free and Boolean convolutions”

New limit theorems related to free multiplicative convolution

Noriyoshi Sakuma, Hiroaki Yoshida (2013)

Studia Mathematica

Similarity:

Let ⊞, ⊠, and ⊎ be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure μ on [0,∞) with finite second moment, we find a scaling limit of ( μ ⊠ N ) ⊞ N as N goes to infinity. The -transform of its limit distribution can be represented by Lambert’s W-function. From this, we deduce that the limiting distribution is freely infinitely divisible, like the lognormal distribution in the classical case. We also show a similar limit theorem by...

On free Boolean vectors.

Mijajlović, Žarko (1998)

Publications de l'Institut Mathématique. Nouvelle Série

Similarity:

Generalized free products

J. D. Monk (2001)

Colloquium Mathematicae

Similarity:

A subalgebra B of the direct product ∏ i ∈ I A i of Boolean algebras is finitely closed if it contains along with any element f any other member of the product differing at most at finitely many places from f. Given such a B, let B* be the set of all members of B which are nonzero at each coordinate. The generalized free product corresponding to B is the subalgebra of the regular open algebra with the poset topology on B* generated by the natural basic open sets. Properties of this product are...

Remarks on the boolean convolution and Kerov's α-transformation

Anna Dorota Krystek (2006)

Banach Center Publications

Similarity:

This paper consists of two parts. The first part is devoted to the study of continuous diagrams and their connections with the boolean convolution. In the second part we investigate the rectangular Young diagrams and respective discrete measures. We recall the definition of Kerov's α-transformation of diagrams, define the α-transformation of finitely supported discrete measures and generalize the notion of the α-transformation.

Maximal free sequences in a Boolean algebra

J. D. Monk (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study free sequences and related notions on Boolean algebras. A free sequence on a BA A is a sequence 〈 a ξ : ξ < α 〉 of elements of A , with α an ordinal, such that for all F , G ∈ [ α ] < ω with F < G we have ∏ ξ ∈ F a ξ · ∏ ξ ∈ G - a ξ ≠ 0 . A free sequence of length α exists iff the Stone space Ult ( A ) has a free sequence of length α in the topological sense. A free sequence is maximal iff it cannot be extended at the end to a longer free sequence. The main notions studied here are the spectrum function 𝔣 sp ( A ) = { | α | : A has an infinite maximal free sequence of length α } and the associated min-max function 𝔣 ( A ) = min ( 𝔣 sp ( A ) ) . Among...

Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

Wojciech Młotkowski, Noriyoshi Sakuma (2011)

Banach Center Publications

Similarity:

We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ( μ ₁ ⨄ μ ₂ ) s = μ ₁ s ⨄ μ ₂ s and if ν₁,ν₂ are symmetric then ( ν ₁ ⨄ ν ₂ ) ( 2 ) = ν ₁ ( 2 ) ⨄ ν ₂ ( 2 ) . Finally we investigate necessary and sufficient conditions under which the latter equality holds.

On some generalization of the t-transformation

Anna Dorota Krystek (2010)

Banach Center Publications

Similarity:

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...