Joint free energy distribution in the random directed polymer problem

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 $\bar{F}$ 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 $\bar{F}$, 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

References in corpus (3)

• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Optimal fluctuation approach to a directed polymer in a random medium
• Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube

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