Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane

Dan-Virgil Voiculescu ()
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Dan-Virgil Voiculescu: University of California at Berkeley

Journal of Theoretical Probability, 2017, vol. 30, issue 1, 384-394

Abstract: Abstract We compute the bi-free max-convolution which is the operation on bivariate distribution functions corresponding to the max-operation with respect to the spectral order on bi-free bipartite 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.

Keywords: Bi-free independence; Bi-free extremal convolution; Two-faced pairs; Primary: 46L54; Secondary: 60G70; 46L53 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-015-0635-7

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