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

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  • Dan-Virgil Voiculescu

    (University of California at Berkeley)

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.

Suggested Citation

  • Dan-Virgil Voiculescu, 2017. "Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane," Journal of Theoretical Probability, Springer, vol. 30(1), pages 384-394, March.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:1:d:10.1007_s10959-015-0635-7
    DOI: 10.1007/s10959-015-0635-7
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    References listed on IDEAS

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    1. Florent Benaych-Georges & Thierry Cabanal-Duvillard, 2010. "A Matrix Interpolation between Classical and Free Max Operations. I. The Univariate Case," Journal of Theoretical Probability, Springer, vol. 23(2), pages 447-465, June.
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