  The random-force (Larkin) model of a directed elastic string subject to
quenched random forces in the transverse directions has been a paradigm in the
statistical physics of disordered systems. In this brief note, we investigate a
modified version of the above model where the total transverse force along the
polymer contour and the related total torque, in each realization of disorder,
vanish. We discuss the merits of adding these constraints and show that they
leave the qualitative behavior in the strong stretching regime unchanged, but
they reduce the effects of the random force by significant numerical
prefactors. We also show that a transverse random force effectively makes the
filament softer to compression by inducing undulations. We calculate the
related linear compression coefficient in both the usual and the constrained
random force model.
