  We study an ensemble of closed random paths, embedded in R^3, with a
curvature dependent action. Previous analytical results indicate that there is
no crumpling transition for any finite value of the curvature coupling.
Nevertheless, in a high statistics numerical simulation, we observe two
different regimes for the specific heat separated by a rather smooth structure.
The analysis of this fact warns us about the difficulties in the interpretation
of numerical results obtained in cases where theoretical results are absent and
a high statistics simulation is unreachable. This may be the case of random
surfaces.
