  We consider the Random Walk Pinning Model studied in [3,2]: this is a random
walk X on Z^d, whose law is modified by the exponential of \beta times
L_N(X,Y), the collision local time up to time N with the (quenched) trajectory
Y of another d-dimensional random walk. If \beta exceeds a certain critical
value \beta_c, the two walks stick together for typical Y realizations
(localized phase). A natural question is whether the disorder is relevant or
not, that is whether the quenched and annealed systems have the same critical
behavior. Birkner and Sun proved that \beta_c coincides with the critical point
of the annealed Random Walk Pinning Model if the space dimension is d=1 or d=2,
and that it differs from it in dimension d\ge4 (for d\ge 5, the result was
proven also in [2]). Here, we consider the open case of the marginal dimension
d=3, and we prove non-coincidence of the critical points.
