## Bernoulli

### Rigid stationary determinantal processes in non-Archimedean fields

Yanqi Qiu

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 25, Number 1 (2019), 75-88.

Dates
First available in Project Euclid: 12 December 2018

https://projecteuclid.org/euclid.bj/1544605239

Digital Object Identifier
doi:10.3150/17-BEJ953

Zentralblatt MATH identifier
07007200

#### Citation

Qiu, Yanqi. Rigid stationary determinantal processes in non-Archimedean fields. Bernoulli 25 (2019), no. 1, 75--88. doi:10.3150/17-BEJ953. https://projecteuclid.org/euclid.bj/1544605239

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