Infinite divisibility for the conditionally free convolution

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.