Gaussian fluctuations of generalized $U$-statistics and subgraph counting in the binomial random-connection model

Qingwei Liu, Nicolas Privault

We derive normal approximation bounds for generalized $U$-statistics of the form \begin{equation*} S_{n,k}(f):=\sum_{ 1 \leq β(1),\dots,β(k) \leq n \atop β(i)\neβ(j), \ 1\leq i\ne…