A dynamical Borel–Cantelli lemma for stationary determinantal processes
Pub. online: 24 September 2026
Type: Research Article
Open Access
Open Access
Received
29 May 2026
29 May 2026
Revised
7 September 2026
7 September 2026
Accepted
7 September 2026
7 September 2026
Published
24 September 2026
24 September 2026
Abstract
We study dynamical Borel–Cantelli properties for the left shift on the binary symbolic space equipped with a stationary determinantal measure generated by a Toeplitz convolution kernel. For sequences of cylinder sets whose measures have a divergent sum, we give sufficient conditions ensuring infinitely many visits almost surely. Under exponential decay of the Fourier coefficients and a uniform nondegeneracy assumption, we also establish the strong Borel–Cantelli property.
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