Linear rigidity of stationary stochastic processes
We consider stationary stochastic processes (Formula presented.) such that (Formula presented.) lies in the closed linear span of (Formula presented.); 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 linearly rigid, that the spectral density vanishes at zero and belongs to the Zygmund class (Formula presented.). We next give a sufficient condition for stationary determinantal point processes on (Formula presented.) and on (Formula presented.) to be linearly rigid. Finally, we show that the determinantal point process on (Formula presented.) induced by a tensor square of Dyson sine kernels is not linearly rigid.