Open Access
February 2019 Rigid stationary determinantal processes in non-Archimedean fields
Yanqi Qiu
Bernoulli 25(1): 75-88 (February 2019). DOI: 10.3150/17-BEJ953


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.


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Yanqi Qiu. "Rigid stationary determinantal processes in non-Archimedean fields." Bernoulli 25 (1) 75 - 88, February 2019.


Received: 1 February 2017; Published: February 2019
First available in Project Euclid: 12 December 2018

zbMATH: 07007200
MathSciNet: MR3892312
Digital Object Identifier: 10.3150/17-BEJ953

Keywords: Non-Archimedean local field , rigidity , stationary determinantal point processes

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 1 • February 2019
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