Stationary determinantal processes: ψ-mixing property and correlation dimensions

Shilei Fan, Lingmin Liao and Yanqi Qiu

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 1-22

Abstract: We study the stationary determinantal processes on the integer lattice, induced by strictly positive and strictly contractive convolution kernels. A necessary and sufficient condition of ψ-mixing property for such a process is given. Some new results on the correlation dimension of the stationary determinantal measure on the symbolic space are obtained. As an application, the precise decreasing rate of the shortest distances between two orbits in the corresponding dynamical system is obtained.

Keywords: Determinantal point processes; ψ-mixing; Correlation dimension (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.05.009

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