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Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane (1505.05020v3)

Published 19 May 2015 in math.OA, math.FA, and math.PR

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.

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