  In this paper, we determine the distribution of the length partition of a
random multicurve of fixed topological type on a closed hyperbolic surface
using the methods of Margulis' thesis and Mirzakhani's equidistribution theorem
for horospheres. This distribution admits a polynomial density, whose
coefficients can be expressed explicitly in terms of intersection numbers of
psi-classes on the Deligne--Mumford compactification, and in particular it does
not depend on the hyperbolic metric. This result generalizes prior work of M.
Mirzakhani in the case of random pants decompositions. Results very close to
ours are obtained independently and simultaneously by F. Arana-Herrera.
