t-deformed convolution and cumulants on formal power series yield LLN and CLT analogues that recover classical convolution at t=-1 and finite free generators at t=d, with explicit infinitesimal generators for the associated semigroups.
Lehner, Free Cumulants and Enumeration of Connected Partitions , Euro- pean Journal of Combinatorics 23 (2002), no
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Convolution, cumulants and infinitesimal generators in the formal power series ring
t-deformed convolution and cumulants on formal power series yield LLN and CLT analogues that recover classical convolution at t=-1 and finite free generators at t=d, with explicit infinitesimal generators for the associated semigroups.