Generalized Wick Decompositions
Chris MacLeod Evgenia Nitishinskaya Buck Shlegeris
We review the cumulant decomposition (a way of decomposing the expectation of
a product of random variables (e.g. $\mathbb{E}[XYZ]$) into a sum of terms
corresponding to partitions of these variables.) and the Wick decomposition (a
way of decomposing a product of (not necessarily random) variables into a sum
of terms corresponding to subsets of the variables). Then we generalize each
one to a new decomposition where the product function is generalized to an
arbitrary function.