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https://www.cimat.mx/reportes/enlinea/I-08-20.pdf
support and for probability measures having all moments and zero mean. We extend the S-transform to symmetric probability measures with unbounded support and without mo-ments. As an application, a representation of symmetric free stable measures is derived as a multiplicative convolution of the semicircle measure with a positive free stable ...
https://en.wikipedia.org/wiki/Free_convolution
Free convolution is the free probability analog of the classical notion of convolution of probability measures. Due to the non-commutative nature of free probability theory, one has to talk separately about additive and multiplicative free convolution, which arise from addition and multiplication of free random variables (see below; in the classical case, what would be the analog of free ...
https://math.stackexchange.com/questions/533537/convolution-of-functions-with-compact-support
$\begingroup$ I suppose if f has compact support K1, g has compact support k2, then fg should have compact support on (k1 intersect k2). But I can't prove it rigorously in the sense of I try to use Holder's inequality to prove that f g is zero on the complement of (k1 intersect k2), but on the other hand, I cannot show that f*g is non zero on ...
https://www.researchgate.net/publication/255663430_The_S-transform_of_symmetric_probability_measures_with_unbounded_supports
We extend the S-transform to symmetric probability measures with unbounded support and without mo- ments. ... of the S-transform of symmetric probability measures ... Free convolution o f measures ...
http://www.ams.org/journals/proc/2009-137-09/S0002-9939-09-09841-4/home.html
We extend the -transform to symmetric probability measures with unbounded support and without moments. As an application, a representation of symmetric free stable measures is derived as a multiplicative convolution of the semicircle measure with a positive free stable measure.
https://link.springer.com/chapter/10.1007/978-3-0348-8779-3_3
Abstract. Free additive convolution is a binary operation on the set M of all probability measures on the real line R. This operation was first defined in [7] for measures with finite moments of all orders (in particular for compactly supported measures).Cited by: 55
https://www.researchgate.net/publication/230877513_Limit_Theorems_for_Monotonic_Convolution_and_the_Chernoff_Product_Formula
Limit Theorems for Monotonic Convolution and the Chernoff Product Formula ... Free convolution of measures with unbounded support. ... and Dan Voiculescu, Free convolution of measures with ...
https://projecteuclid.org/euclid.ejp/1538618571
We consider different limit theorems for additive and multiplicative free Lévy processes. The main results are concerned with positive and unitary multiplicative free Lévy processes at small times, showing convergence to log free stable laws for many examples.Cited by: 1
https://arxiv.org/abs/1211.4457
In classical probability the law of large numbers for the multiplicative convolution follows directly from the law for the additive convolution. In free probability this is not the case. The free additive law was proved by D. Voiculescu in 1986 for probability measures with bounded support and extended to all probability measures with first moment by J. M. Lindsay and V. Pata in 1997, while ...Cited by: 20
https://link.springer.com/chapter/10.1007/978-3-642-39459-1_8
Aug 25, 2013 · The free additive law was proved by D. Voiculescu in 1986 for probability measures with bounded support and extended to all probability measures with first moment by J.M. Lindsay and V. Pata in 1997, while the free multiplicative law was proved only recently by G. Tucci in 2010.Cited by: 20
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