Bernoulli

Rigid stationary determinantal processes in non-Archimedean fields

Yanqi Qiu

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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
Received: February 2017
First available in Project Euclid: 12 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1544605239

Digital Object Identifier
doi:10.3150/17-BEJ953

Zentralblatt MATH identifier
07007200

Keywords
non-Archimedean local field rigidity stationary determinantal point processes

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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