报告摘要：
| In noncommutative probability, independence relations between random variables provide specific rules for calculations of all mixed moments of those random variables. Recently, Voiculescu started a program of studying pairs of random variables. In this talk, we construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce free-Boolean cumulants and show that free-Boolean independence is equivalent to the vanishing of mixed cumulants.
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