  The a.s. existence of a polymer probability in the infinite volume limit is
readily obtained under general conditions of weak disorder from standard theory
on multiplicative cascades or branching random walk. However, speculations in
the case of strong disorder have been mixed. In this note existence of an
infinite volume probability is established at critical strong disorder for
which one has convergence in probability. Some calculations in support of a
specific formula for the a.s. asymptotic variance of the polymer path under
strong disorder are also provided.
