%0 Unpublished work
%T Linear rigidity of stationary stochastic processes
%+ Institut de Mathématiques de Marseille (I2M)
%+ Probabilités, statistique, physique mathématique (PSPM)
%+ Analyse fonctionnelle (AF)
%A Bufetov, Alexander I.
%A Dabrowski, Yoann
%A Qiu, Yanqi
%8 2016-01-14
%D 2016
%Z Mathematics [math]/Dynamical Systems [math.DS]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://hal.science/hal-01256215/document
%2 https://hal.science/hal-01256215/file/Linear-rigid.pdf
%L hal-01256215
%U https://hal.science/hal-01256215
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