A ug 2 00 6 DECOMPOSITIONS OF THE FREE ADDITIVE CONVOLUTION
نویسنده
چکیده
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive convolution μ` ν of compactly supported probability measures in free probability. These decompositions are directly related to alternating decompositions of the associated subordination functions. In particular, they allow us to compute free additive convolutions of compactly supported measures without using free cumulants or R-transforms. In simple cases, representations of Cauchy transforms Gμ` νpzq as continued fractions are obtained in a natural way. Moreover, this approach establishes a clear connection between convolutions and products associated with the main notions of independence (free, monotone and boolean) in noncommutative probability. Finally, our result leads to natural decompositions of the free product of rooted graphs. Mathematics Subject Classification (2000): 46L54, 46L53
منابع مشابه
Decompositions of the Free Additive Convolution
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive convolution μ` ν of compactly supported probability measures in free probability. These decompositions are directly related to alternating decompositions of the ...
متن کاملOperators Related to Subordination for Free Multiplicative Convolutions
It has been shown by Voiculescu and Biane that the analytic subordination property holds for free additive and multiplicative convolutions. In this paper, we present an operatorial approach to subordination for free multiplicative convolutions. This study is based on the concepts of ‘freeness with subordination’, or ‘s-free independence’, and ‘orthogonal independence’, introduced recently in th...
متن کاملar X iv : h ep - t h / 04 06 15 4 v 5 2 8 A ug 2 00 6 Characters of the Positive Energy UIRs of D = 4 Conformal Supersymmetry
We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of...
متن کاملm at h . O A ] 1 7 N ov 2 00 6 RECTANGULAR RANDOM MATRICES , RELATED CONVOLUTION
We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically free with amalgamation over a subalgebra. Therefore we can define a “rectangular free convolution”, linearized by cumulants and by an analytic integral...
متن کاملA ug 2 00 6 The average behaviour of financial market by 2 scale homogenisation
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short terms. A diffusion equation with a time dependent diffusion coefficient that des...
متن کامل