Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane
arXiv:1505.05020
Abstract
We compute the bi-free max-convolution which is the operation on bi-variate distribution functions corresponding to the max-operation with respect to the spectral order on bi-free bi-partite two-faced pairs of hermitian non-commutative random variables. With the corresponding definitions of bi-free max-stable and max-infinitely-divisible laws their determination becomes in this way a classical analysis question.
12 pages, minor corrections and further very minor corrections. Paper to appear in Journal of Theoretical Probability