Takahiro Hasebe

Classical and free infinite divisibility for Boolean stable laws

We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index

Relations between cumulants in noncommutative probability

\alpha

CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS

and an asymmetry coefficient

Unimodality of the Freely Selfdecomposable Probability Laws

\rho

Fock space associated to Coxeter groups of type B

. We prove that the Boolean stable law is freely infinitely divisible if and only if one of the following conditions holds:

Free infinite divisibility for beta distributions and related ones

0<\alpha\leq\frac{1}{2}

Unimodality of Boolean and Monotone Stable Distributions

;

Order quasisymmetric functions distinguish rooted trees

\frac{1}{2}<\alpha\leq\frac{2}{3}

FOURIER AND CAUCHY–STIELTJES TRANSFORMS OF POWER LAWS INCLUDING STABLE DISTRIBUTIONS

and

Limit theorems in bi-free probability theory

2-\frac{1}{\alpha}\leq\rho \leq \frac{1}{\alpha}-1