Rigid stationary determinantal processes in non-Archimedean fields

Yanqi Qiu

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

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

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non-Archimedean local field rigidity stationary determinantal point processes


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

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  • [1] Bufetov, A.I. (2016). Rigidity of determinantal point processes with the Airy, the Bessel and the gamma kernel. Bull. Math. Sci. 6 163–172.
  • [2] Bufetov, A.I., Dabrowski, Y. and Qiu, Y. (2015). Linear rigidity of stationary stochastic processes. Ergodic Theory Dynam. Systems. To appear. Available at arXiv:1507.00670.
  • [3] Bufetov, A.I. and Qiu, Y. (2017). Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields. Compos. Math. 153 2482–2533.
  • [4] Bufetov, A.I. and Qiu, Y. (2017). Determinantal point processes associated with Hilbert spaces of holomorphic functions. Comm. Math. Phys. 351 1–44.
  • [5] Ghosh, S. (2015). Determinantal processes and completeness of random exponentials: The critical case. Probab. Theory Related Fields 163 643–665.
  • [6] Ghosh, S. and Krishnapur, M. (2015). Rigidity hierarchy in random point fields: Random polynomials and determinantal processes. Available at arXiv:1510.08814.
  • [7] Ghosh, S. and Peres, Y. (2017). Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues. Duke Math. J. 166 1789–1858.
  • [8] Hough, J.B., Krishnapur, M., Peres, Y. and Virág, B. (2006). Determinantal processes and independence. Probab. Surv. 3 206–229.
  • [9] Lyons, R. (2003). Determinantal probability measures. Publ. Math. Inst. Hautes Études Sci. 98 167–212.
  • [10] Macchi, O. (1975). The coincidence approach to stochastic point processes. Adv. in Appl. Probab. 7 83–122.
  • [11] Osada, H. and Shirai, T. (2016). Absolute continuity and singularity of Palm measures of the Ginibre point process. Probab. Theory Related Fields 165 725–770.
  • [12] Ramakrishnan, D. and Valenza, R.J. (1999). Fourier Analysis on Number Fields. Graduate Texts in Mathematics 186. New York: Springer.
  • [13] Soshnikov, A. (2000). Determinantal random point fields. Uspekhi Mat. Nauk 55 107–160.