| Abstract: |
| Recently, we have shown that the partition function of the directed polymer
model on Z^{2+1} admits a phase transition in a suitable continuum and weak disorder limit.
In particular, the partition function converges in law to a log-normal distribution below
the critical point, and converges to 0 at and above the critical point. Here we focus on a
suitable window around the critical point, and we prove that the space-averaged point-to-plane
partition function has a uniformly bounded third moment. As a consequence, when
interpreted as a random measure on R^2, the rescaled point-to-plane partition functions have
non-trivial limit points, and each limit point has the same explicit covariance structure. |
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