论文标题
慢慢生长序列的完整泊松局部统计数据
Full Poissonian Local Statistics of Slowly Growing Sequences
论文作者
论文摘要
修复$α> 0 $，然后由Fejér的定理$（α（\ log n）^{a} \，\ mathrm {mod} \，1）_ {n \ geq1} $在且仅在$ a> 1 $时仅在且仅在$ a> 1 $时。我们通过表明所有相关功能以及差距分布都提供了Poissonian提供的$ a> 1 $来提高这一点。这是确定性序列模型的第一个示例，其差距分布，并且所有相关性被证明是泊松人。 $ a $的范围是最佳的，并补充了Marklof和Strömbergsson的结果，他们发现了$（log（n）\，\ Mathrm {mod} \，1）$的限制差距分布，这一定不是Poissonian。
Fix $α>0$, then by Fejér's theorem $ (α(\log n)^{A}\,\mathrm{mod}\,1)_{n\geq1}$ is uniformly distributed if and only if $A>1$. We sharpen this by showing that all correlation functions, and hence the gap distribution, are Poissonian provided $A>1$. This is the first example of a deterministic sequence modulo one whose gap distribution, and all of whose correlations are proven to be Poissonian. The range of $A$ is optimal and complements a result of Marklof and Strömbergsson who found the limiting gap distribution of $(\log(n)\, \mathrm{mod}\,1)$, which is necessarily not Poissonian.
