Author

Qing-Long Zhou

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Preprint Oct 2026

Metric Poissonian Pair Correlation Property Part 2: The Case $n\log n$

We prove that $(\alpha n\log n)_{n\ge1}$ has Poissonian pair correlation for almost every real $\alpha$, solving a Problem posed by Aistleitner, El-Baz and Munsch [Open Problem 3, Geom. Funct. Anal. 2021]. Our main contribution is a new four-point counting estimate with a fixed power saving over $N^{7/3}$ at tolerance...

Bo Tan, Zhen Zhang, Qing-Long Zhou · 1 citation

Preprint Oct 2026

Poissonian Pair Correlation for Bernoulli Orbits

Let $\alpha, \beta \in \mathbb{T} = \mathbb{R}/\mathbb{Z}$, and let $(\xi_n)_{n \ge 1}$ be independent random variables taking the values $\alpha$ and $\beta$ with equal probability. We study the random walk \[X_n = \xi_1 + \cdots + \xi_n \pmod 1\] and present a deterministic Diophantine condition on \((\alpha,...

Bo Tan, Zhen Zhang, Qing-Long Zhou · 0 citations

Qing-Long Zhou

Metric Poissonian Pair Correlation Property Part 2: The Case \(n\log n\)

Poissonian Pair Correlation for Bernoulli Orbits