Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations

@article{EbrahimiFard2020OperadsO,
  title={Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations},
  author={K. Ebrahimi-Fard and L. Foissy and Joachim Kock and F. Patras},
  journal={Advances in Mathematics},
  year={2020},
  volume={369},
  pages={107170}
}
Abstract We establish and explore a relationship between two approaches to moment-cumulant relations in free probability theory: on one side the main approach, due to Speicher, given in terms of Mobius inversion on the lattice of noncrossing partitions, and on the other side the more recent non-commutative shuffle-algebra approach, where the moment-cumulant relations take the form of certain exponential-logarithm relations. We achieve this by exhibiting two operad structures on (noncrossing… Expand
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