Abstract
We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution.
Institutions
Move through the context
Research map
Move through nearby people, institutions, topics and adjacent work without leaving the paper page.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Structured reviews
0 review(s)
ContributeLeave structured feedbackUse the review template when you have a concrete strength, concern or method question.
No structured reviews yet. High-signal critique starts here.
Work discussion
0 comment(s)
DiscussAdd a commentKeep quick notes, caveats and replication pointers separate from formal reviews.
No discussion yet. The first strong comment sets the tone.