  We write down a one-dimensional integral formula and compute large-n
asymptotics for the expectation of the absolute value of the smallest component
of a unit vector in n-dimensional Euclidean space.
  The method is general, and allows to write the mean over the sphere of an
homogeneous function in terms of an expectation of a function of independent,
identically distributed Gaussians. We also write down an asymptotic formula for
the minimum of a large number of identical independent positive random
variables.
