Abstract
We revive the concept of \({\Lambda}\)-freeness of Młotkowski (Quant Prob Relat Top 7:27–41, 2004), which describes a mixture of classical and free independence between algebras of random variables. In particular, we give a description of this in terms of cumulants; this will be instrumental in the subsequent paper (Speicher and Weber, Quantum groups with partial commutation relations, 2016) where the quantum symmetries underlying these mixtures of classical and free independences will be considered.
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R. Speicher is supported by the ERC-Advanced Grant “Non-commutative Distributions in Free Probability”.
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Speicher, R., Wysoczański, J. Mixtures of classical and free independence. Arch. Math. 107, 445–453 (2016). https://doi.org/10.1007/s00013-016-0955-6
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DOI: https://doi.org/10.1007/s00013-016-0955-6