Results 1 to 10 of about 460 (26)
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Special Matrices, 2015 In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
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Matrices induced by arithmetic functions acting on certain Krein spaces
Special Matrices, 2017 In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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On free stable distributions [PDF]
, 2014 We investigate the analytical properties of free stable distributions and discover many connections with the classical stable distributions. Our main results include an explicit formula for the Mellin transform, series representations for the ...
Hasebe, Takahiro, Kuznetsov, Alexey
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, 2010 In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean, and especially, monotone probability theories.
Hasebe, Takahiro, Saigo, Hayato
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Multidimensional limit theorems for homogeneous sums: a general transfer principle [PDF]
, 2015 The aim of the present paper is to establish the multidimensional counterpart of the \textit{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic random variables (that is, having positive and zero fourth cumulant ...
Nourdin, Ivan +3 more
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Central Limit Theorems for the Brownian motion on large unitary groups [PDF]
, 2009 In this paper, we are concerned with the large N limit of linear combinations of the entries of a Brownian motion on the group of N by N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one.
De France +3 more
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On Explicit Probability Densities Associated with Fuss-Catalan Numbers
, 2010 In this note we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers.
Liu, Dang-Zheng +2 more
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Remarks on free mutual information and orbital free entropy [PDF]
, 2013 The present notes provide a proof of $i^*(\mathbb{C}P+\mathbb{C}(I-P)\,;\mathbb{C}Q+\mathbb{C}(I-Q)) = -\chi_\mathrm{orb}(P,Q)$ for any pair of projections $P,Q$ with $\tau(P)=\tau(Q)=1/2$.
Izumi, Masaki, Ueda, Yoshimichi
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Asymptotic freeness in tracial ultraproducts
Forum of Mathematics, SigmaWe prove novel asymptotic freeness results in tracial ultraproduct von Neumann algebras. In particular, we show that whenever $M = M_1 \ast M_2$ is a tracial free product von Neumann algebra and $u_1 \in \mathscr U(M_1)$ , $u_2 \in ...
Cyril Houdayer, Adrian Ioana
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