Poissonian correlations of $\hat{I}\pm n^d$ mod $1$

Chris Lutsko, Nick Rome, Niclas Technau

Let $x(n):=\hat{I}\pm n^d\mathrm{mod}1$ for integer $d>1$ and non-zero real $\hat{I}\pm$. We show that $\{x(n){\}}_{n>0}$ has Poissonian $\ell$-point correlations for almost all choices of $\hat{I}\pm$ when $d$ i…