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 $\widehat{ \mathbb{ 1}}_S(x-y)$, where $\widehat{ \mathbb{ 1}}_S$ is the Fourier transform of the indicator function $\mathbb{ 1}_S$. 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.
Categories: math.PR math.FA