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Beschreibung:
First we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function C(x,y) defining an alpha-determinantal point process (DPP). Assuming absolute integrability of the function C_0(x) = C(o,x) we show that a stationary alpha-DPP with kernel function C_0(x) is "strongly" Brillinger-mixing implying, among others, that its tail-sigma-field is trivial. Second we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications to statistical second-order analysis of alpha-DPPs.