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Let $F$ be a non-discrete non-Archimedean local field. For any subset $S\subset F$ with finite Haar measure, there is a stationary determinantal point process on $F$ with correlation kernel $\widehat{\mathbbm{1}}_S(x-y)$, where $\widehat{\mathbbm{1}}_S$ is the Fourier transform of the indicator function $\mathbbm{1}_S$. In this note, we give a geometrical condition on the subset $S$, such that the associated determinantal point process is rigid in the sense of Ghosh and Peres. Our geometrical condition is very different from the Euclidean case.

Rigid stationary determinantal processes in non-Archimedean fields