The Central Limit Theorem in probability theory says that the sum of a sequence of i.i.d. random variables X(k) with finite second is asymptotically normal. If we instead take a function f(x,y) of two variables and compute the sum over all pairs of X(i) and X(j), then the limiting law will depend on the level of degeneracy of f. In this talk, by developing a combinatorial framework and using the cumulant approach, we investigate this phenomenon (known as Wiener Chaos Decomposition) for determinantal point process, which then involves an operator formulation.
