  The assumption that the elements of the cost matrix in the classical
assignment problem are drawn independently from a standard Gaussian
distribution motivates the study of a particular Gaussian field indexed by the
symmetric permutation group.
  The correlation structure of the field is determined by the Hamming distance
between two permutations.
  The expectation of the maximum of the field is shown to go to infinity in the
same way as if all variables of the field were independent.
  However, the variance of the maximum is shown to converge to zero at a rate
which is slower than under independence, as the variance cannot be smaller than
the one of the cost of the average assignment.
  Still, the convergence to zero of the variance means that the maximum
possesses a property known as superconcentration.
  Finally, the dimension of the set of near-optimal assignments is shown to
converge to zero.
