Joint free energy distribution in the random directed polymer problem
arXiv:0705.0220 · doi:10.1103/PhysRevLett.100.050601
Abstract
We consider two configurations of a random directed polymer of length L confined to a plane and ending in two points separated by 2u. Defining the mean free energy and the free energy difference F' of the two configurations, we determine the joint distribution function P_{L,u}(\bar F,F') using the replica approach. We find that for large L and large negative free energies , the joint distribution function factorizes into longitudinal (P_{L,u} (\bar F)) and transverse (P_{u}(F')) components, which furthermore coincide with results obtained prevously via different independent routes.
4 pages, 1 figure