  We study the one-body reduced density matrix of a system of $N$
one-dimensional impenetrable anyons trapped by a harmonic potential. To this
purpose we extend two methods developed to tackle related problems, namely the
determinant approach and the replica method. While the former is the basis for
exact numerical computations at finite $N$, the latter has the advantage of
providing an analytic asymptotic expansion for large $N$. We show that the
first few terms of such expansion are sufficient to reproduce the numerical
results to an excellent accuracy even for relatively small $N$, thus
demonstrating the effectiveness of the replica method.
