Take $n$ points at random in a fixed set in $R^d$. Define the maximal spacing, e.g., as the volume of the largest ball that is contained in the fixed set and avoids all $n$ chosen points. The asymptotic distribution of the maximal spacing and strong bounds are given.
"Maximal Spacings in Several Dimensions." Ann. Probab. 15 (1) 274 - 280, January, 1987. https://doi.org/10.1214/aop/1176992269