Bivariate fluctuations for the number of arithmetic progressions in random sets

Yacine Barhoumi-Andréani, Christoph Koch, Hong Liu

We study arithmetic progressions $\{a,a+b,a+2b,\dots ,a+(\ell -1)b\}$, with $\ell \ge 3$, in random subsets of the initial segment of natural numbers $[n]:=\{1,2,\dots ,n\}$. Given $…