I have a point, call it $x$, located somewhere in a unit square $[0,1]^2$.
I drawn $n$ new points, all uniformly and independently, all those in the unit square $[0,1]^2$.
What is the expected Euclidean distance between $x$, and the closest of the other $n$ dots?
EDIT: thanks all for your nice replies. I do realize it is incredibly difficult. If the $n$ numbers are drawned from a Poisson point processes, a paper by Holroyd et al. (Poisson point proccesses) shows that the probability that two points are separated by a distance larger than r is
$Pr(Q>r)=\frac{C}{r^{0.49}}$
I was trying to derive this result limiting myself to points in the unit square but it looks hard.