Limit theorems for classical, freely and Boolean max-infinitely divisible distributions

Abstract

We investigate a Belinschi-Nica type semigroup for free and Boolean max-convolutions. We prove that this semigroup at time one connects limit theorems for freely and Boolean max-infinitely divisible distributions. Moreover, we also construct a max-analogue of Boolean-classical Bercovici-Pata bijection, establishing the equivalence of limit theorems for Boolean and classical max-infinitely divisible distributions.

21 pages, accepted by JOTP

Cited by in corpus (2)

• Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution
• Homomorphisms relative to additive convolutions and max-convolutions: free, boolean and classical cases