2010/11/30 by Sylvain Prolhac, Herbert Spohn · 26 citations
Mathematics · Physics and Astronomy · #Airy function #Decoupling (probability) #Distribution function #Generating function #Geometry and complex manifolds #Lattice (music) #Limit (mathematics) #Partition function (quantum field theory) #Probability-generating function #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2011/01/p01031
published in Journal of Statistical Mechanics Theory and Experiment 2011(01), P01031 (Institute of Physics) · 25 pages
openalex publication_date 2011/01/27 · arxiv created 2011/01/28 · arxiv updated 2011/01/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a (1 + 1)-dimensional directed continuum polymer in a Gaussian delta-correlated spacetime random potential. For this model the moments (= replica) of the partition function, Z ( x , t ), can be expressed in terms of the attractive δ-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.