  We find that the probability distribution for the largest intervals $p(l)$
exhibits universal properties for different systems including random walk and
random cutting models. In particular, $p(l)$ has an infinite set of
singularities at $l=1/k$ with $k=2,3,\ldots$ which become weaker and weaker as
$k \to \infty$; additionally, $p(l)$ has an essential singularity at $l=0$.
These properties are found also in many dimensional situation.
