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We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions.
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2007
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J. William Helton, Reza Rashidi Far, and Roland Speicher, Operator-valued semicircular elements: solving a quadratic matrix equation with positivity constraints , Int. Math. Res. Not. IMRN (2007), no. 22, Art. ID rnm086, 15
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Serban T. Belinschi, Mihai Popa, and Victor Vinnikov, Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection , Journal of Functional Analysis, 262
2012
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Serban T. Belinschi, Roland Speicher, John Treilhard, and Carlos Vargas, Operator-valued free multiplicative convolution: analytic subordination theory and applications to random matrix theory
2012
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R. Speicher and C. Vargas, Free deterministic equivalents, rectangular random matrix models, and operator-valued free probability theory , Random Matrices: Theory and Applications 1
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Dimitry Shlyakhtenko and Paul Skoufranis, Freely independent random variables with non-atomic distributions
2013
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