Abstract
In this paper, we show that free cumulants can be naturally seen as the limiting value of ``cumulants of matrices''. We define these objects as functions on the symmetric group by some convolution relations involving the generalized moments. We state that some characteristic properties of the free cumulants already hold for these cumulants.
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Capitaine, M., Casalis, M. Cumulants for random matrices as convolutions on the symmetric group. Probab. Theory Relat. Fields 136, 19–36 (2006). https://doi.org/10.1007/s00440-005-0474-z
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DOI: https://doi.org/10.1007/s00440-005-0474-z