  Every smooth closed curve can be represented by a suitable Fourier sum. We
show that the ensemble of curves generated by randomly chosen Fourier
coefficients with amplitudes inversely proportional to spatial frequency (with
a smooth exponential cutoff), can be accurately mapped on the physical ensemble
of worm-like polymer loops. We find that measures of correlation on the scale
of the entire loop yield a larger persistence length than that calculated from
the tangent-tangent correlation function at small length scales. The conjecture
that physical loops exhibit additional rigidity on scales comparable to the
entire loop due to the contribution of twist rigidity, can be tested
experimentally by determining the persistence length from the local curvature
and comparing it with that obtained by measuring the radius of gyration of
dsDNA plasmids. The topological properties of the ensemble randomly generated
worm-like loops are shown to be similar to that of other polymer models.
