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On the strong Brillinger-mixing property of α -determinantal point processes and some applications

Lothar Heinrich — 2016

Applications of Mathematics

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 α -determinantal point process (DPP). Assuming absolute integrability of the function C 0 ( x ) = C ( o , x ) , we show that a stationary α -DPP with kernel function C 0 ( x ) is “strongly” Brillinger-mixing, implying, among others, that its tail- σ -field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications...

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