Ratio sets of random sets

Javier Cilleruelo, Jorge Guijarro-Ordonez

We study the typical behavior of the size of the ratio set $A/A$ for a random subset $A\subset \{1,\dots ,n\}$. For example, we prove that $|A/A|\sim \frac{2\text{Li}_2(3/4)}{π^2}…