Two-point generating function of the free energy for a directed polymer in a random medium

We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive delta-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x_1,t), Z(x_2,t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the long time behavior of the KPZ equation is the same as derived previously for lattice growth models.

No reviews yet.

No comments yet.