  We describe the scaling limit of the nearest neighbour prudent walk on the
square lattice, which performs steps uniformly in directions in which it does
not see sites already visited. We show that the scaling limit is given by the
process Z(u) = s_1 theta^+(3u/7) e_1 + s_2 theta^-(3u/7) e_2, where e_1, e_2 is
the canonical basis, theta^+(t), resp. theta^-(t), is the time spent by a
one-dimensional Brownian motion above, resp. below, 0 up to time t, and s_1,
s_2 are two random signs. In particular, the asymptotic speed of the walk is
well-defined in the L^1-norm and equals 3/7.
