Probability interpolating between free and boolean
Łukasz Wojakowski
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Łukasz Wojakowski
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Mlotkowski, Wojciech (2010)
Documenta Mathematica
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Wojciech Młotkowski (2002)
Studia Mathematica
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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.
J. Łąski (1976)
Applicationes Mathematicae
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C. V. Stanojević (1973)
Recherche Coopérative sur Programme n°25
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W. Słowikowski
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CONTENTS1. Introduction, review of the results, examples...................................................................................52. Linear probability measures and their representations................................................................103. Linear Lusin measurable functionals...............................................................................................164. Pre-supports and a modification of the definition of the linear probability measure................235....
W. Krakowiak (1980)
Colloquium Mathematicae
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Krakowiak Wiesław
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Introduction.............................................................5I. Preliminaries.........................................................6 1.1. Semigroups........................................7 1.2. Algebraic groups..................................7 1.3. Additive operators in Abelian groups and linear operators in linear spaces................................8 1.4. Abelian metrizable groups........................10 1.5. Locally compact Abelian groups...................13 1.6....
Emile M.J. Bertin, Radu Theodorescu (1984)
Mathematische Annalen
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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]).
Fumio Hiai, Dénes Petz (2006)
Banach Center Publications
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M. S. Bingham, K. R. Parthasarathy (1966-1967)
Publications mathématiques et informatique de Rennes
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Anna Dorota Krystek, Łukasz Jan Wojakowski (2011)
Banach Center Publications
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In this article we discuss the Catalan and super-Catalan (or Schröder) numbers. We start with some combinatorial interpretations of those numbers. We study two probability measures in the context of free probability, one whose moments are super-Catalan, and another, whose even moments are super-Catalan and odd moments are zero. With the use of the latter we also show some new formulae for evaluation of the Catalans in terms of super-Catalans and vice-versa.
Mostafa K. Ardakani, Shaun S. Wulff (2014)
Discussiones Mathematicae Probability and Statistics
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Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...
Kargin, Vladislav (2008)
Electronic Communications in Probability [electronic only]
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R. Z. Buzyakova, A. Chigogidze (2011)
Fundamenta Mathematicae
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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples
Hentzel, I.R., Peresi, L.A. (2006)
Experimental Mathematics
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Romano Scozzafava (1996)
Mathware and Soft Computing
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