- Linear rigidity of stationary stochastic processes hal link

Auteur(s): Bufetov A., Dabrowski Yoann, Qiu Yanqi

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We consider stationary stochastic processes X n , n ∈ Z such that X 0 lies in the closed linear span of X n , n = 0; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we show that it suffices, for a stationary stochastic process to be rigid, that the spectral density vanish at zero and belong to the Zygmund class Λ * (1). We next give sufficient condition for stationary determinantal point processes on Z and on R to be rigid. Finally, we show that the determinantal point process on R 2 induced by a tensor square of Dyson sine-kernels is not linearly rigid.