Results 1 to 10 of about 479 (44)
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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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
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 operator-valued monotone independence [PDF]
, 2014 We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula.
Hasebe, Takahiro, Saigo, Hayato
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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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One-sided Cauchy-Stieltjes Kernel Families [PDF]
, 2010 This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that is unbounded on
Abdelhamid Hassairi +15 more
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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
core +5 more sources
Unimodality of the freely selfdecomposable probability laws [PDF]
, 2015 We show that any freely selfdecomposable probability law is unimodal. This is the free probabilistic analog of Yamazato's result in [Ann. Probab.
Hasebe, Takahiro, Thorbjornsen, Steen
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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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A matrix interpolation between classical and free max operations: I. The univariate case [PDF]
, 2009 Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy:
A.W. Vaart van der +11 more
core +7 more sources