Analytic subordination results in free probability from non-coassociative derivation-comultiplications
Stephen Curran
TL;DR
This paper extends Voiculescu's analytic subordination approach in free probability using non-coassociative derivation-comultiplications, providing new proofs for key subordination results involving freely Markovian triples and free unitaries with amalgamation.
Contribution
It introduces a novel extension of Voiculescu's method to non-coassociative structures, offering new proofs of fundamental subordination results in free probability.
Findings
New proofs of Voiculescu's analytic subordination results
Extension of subordination approach to non-coassociative derivation-comultiplications
Application to freely Markovian triples and free unitaries with amalgamation
Abstract
We extend Voiculescu's approach to analytic subordination through the coalgebra of the free difference quotient to non-coassociative derivation-comultiplications appearing in free probability theory. We obtain new proofs of Voiculescu's analytic subordination results for freely Markovian triples, and for multiplication of unitaries which are free with amalgamation.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Geometric and Algebraic Topology