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Infinite divisibility for the conditionally free convolution

机译：有条件自由卷积的无限除数

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摘要

Infinite divisibility for the free additive convolution was studied in Ref. 20. A complete characterization of boxed plus-infinitely divisible distributions was given, and it was explained in Ref. 21 that this characterization is an analogue of the classical Levy Khintchine characterization. In fact, the analogue of the Gaussian distribution appeared even earlier, when the central limit theorem for free additive convolution was proven in Ref. 19. In this paper we define the notion of c-infinitely divisibility and give the description of infinitely divisible compactly supported probability measures relative to the conditionally free convolution. We also show that the Levy Khintchine measures associated with a c-infinitely divisible distribution p can be calculated, as in the classical or free case, as a weak limit of measures related with the convolution semigroup generated by (mu, 4) for 4- boxed plus- infinitely divisible.
机译：自由加法卷积的无穷除法在参考文献5中进行了研究。 20.给出了方框加无限无限可分分布的完整特征，这在参考文献10中有解释。 21该特征与经典的Levy Khintchine特征类似。实际上，当参考文献中证明了自由加法卷积的中心极限定理时，高斯分布的类似物出现得更早了。 19.在本文中，我们定义了c无限可整性的概念，并给出了关于有条件自由卷积的无限可整紧支持概率概率测度的描述。我们还表明，与经典或自由情况一样，可以计算与c无穷大可分布p相关的Levy Khintchine测度，作为与（mu，4）为4生成的卷积半群相关的测度的弱极限盒装加-无限整除。

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