RIGID STATIONARY DETERMINANTAL PROCESSES IN NON-ARCHIMEDEAN FIELDS

Yanqi Qiu (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Yanqi Qiu. RIGID STATIONARY DETERMINANTAL PROCESSES IN NON-ARCHIMEDEAN FIELDS. Bernoulli, 2019, 25 (1), pp.75-88. ⟨10.3150/17-BEJ953⟩. ⟨hal-01483633⟩