  Recent Monte Carlo simulations of a grafted semiflexible polymer in 1+1
dimensions have revealed a pronounced bimodal structure in the probability
distribution of the transverse (bending) fluctuations of the free end, when the
total contour length is of the order of the persistence length [G. Lattanzi et
al., Phys. Rev E 69, 021801 (2004)]. In this paper, we show that the emergence
of bimodality is related to a similar behavior observed when a random walker is
driven in the transverse direction by a certain type of shear flow. We adapt an
effective-medium argument, which was first introduced in the context of the
sheared random-walk problem [E. Ben-Naim et al., Phys. Rev. A 45, 7207 (1992)],
in order to obtain a simple analytic approximation of the probability
distribution of the free-end fluctuations. We show that this approximation
captures the bimodality and most of the qualitative features of the free-end
fluctuations. We also predict that relaxing the local inextensibility
constraint of the wormlike chain could lead to the disappearence of bimodality.
