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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.00793 |
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Table of Contents:
- We study the statistics of pairs from the sequence $(n^α)_{n\in\mathbb{N}^*}$, for every parameter $α\in \, ]0,1[$. We prove the convergence of the empirical pair correlation measures towards a measure with an explicit density. In particular, when using the scaling factor $N\mapsto N^{1-α}$, we prove that there exists an exotic pair correlation function which exhibits a level repulsion phenomenon. For other scaling factors, we prove that either the pair correlations are Poissonian or there is a total loss of mass. In addition, we give an error term for this convergence.