Results 1 to 10 of about 490 (43)

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.
doaj   +1 more source

The Monotone Cumulants [PDF]

, 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
core   +5 more sources

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.
doaj   +1 more source

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
core   +3 more sources

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
doaj   +1 more source

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, Peccati, Giovanni, Poly, Guillaume, Simone, Rosaria   +3 more
core   +5 more sources

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
core   +1 more source

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, Song, Chunwei, Wang, Zheng-Dong   +2 more
core   +1 more source

Rectangular R-transform as the limit of rectangular spherical integrals [PDF]

, 2011
In this paper, we connect rectangular free probability theory and spherical integrals. In this way, we prove the analogue, for rectangular or square non-Hermitian matrices, of a result that Guionnet and Maida proved for Hermitian matrices in 2005.
Benaych-Georges, Florent
core   +3 more sources

Asymptotic freeness in tracial ultraproducts

Forum of Mathematics, Sigma
We 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
doaj   +1 more source