The minimum of gaps generated by random packing of unit intervals into a large interval.

Let L(x) be the random variable which represents the minimum of the lengths of the gaps generated by random packing of unit intervals into [0,x]. It is known that for 01 there exists a(h)>0 such that x(-1) integral (o -> x) exp[a(h)(y+1)]Pr{L (y)>/h}dy->1 as x->oo. Approximations to a(h) are derived by singular perturbation techniques when h is small, and when h is close to 1. A numerical scheme for evaluating a(h) is also presented, and a table of values is given.