  The Frobenius number F(a) of an integer vector a with positive coprime
coefficients is defined as the largest number that does not have a
representation as a positive integer linear combination of the coefficients of
a. We show that if a is taken to be random in an expanding d-dimensional
domain, then F(a) has a limit distribution, which is given by the probability
distribution for the covering radius of a certain simplex with respect to a
(d-1)-dimensional random lattice. This result extends recent studies for d=3 by
Arnold, Bourgain-Sinai and Shur-Sinai-Ustinov. The key features of our approach
are (a) a novel interpretation of the Frobenius number in terms of the dynamics
of a certain group action on the space of d-dimensional lattices, and (b) an
equidistribution theorem for a multidimensional Farey sequence on closed
horospheres.
