Stationary determinantal processes: $\psi$-mixing property and $L^q$-dimensions

Shilei Fan; Lingmin Liao; Yanqi Qiu

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arXiv · 1911.04718

Stationary determinantal processes: $\psi$-mixing property and $L^q$-dimensions

Shilei Fan·Lingmin Liao·Yanqi Qiu

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Abstract

The results of this paper are 3-folded. Firstly, for any stationary determinantal process on the integer lattice, induced by strictly positive and strictly contractive involution kernel, we obtain the necessary and sufficient condition for the $\psi$-mixing property. Secondly, we obtain the existence of the $L^q$-dimensions of the stationary determinantal measure on symbolic space $\{0, 1\}^\mathbb{N}$ under appropriate conditions. Thirdly, the previous two results together imply the precise increasing rate of the longest common substring of a typical pair of points in $\{0, 1\}^\mathbb{N}$.

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BibTeX RIS

Shilei Fan, Lingmin Liao, Yanqi Qiu. 2019-11-12. Stationary determinantal processes: $\psi$-mixing property and $L^q$-dimensions. https://arxiv.org/abs/1911.04718

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