2014/09/19 by Francis Comets, Comets, Francis, Vu Lan Nguyen +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR
paper · pdf · doi:10.48550/arxiv.1409.5754
33 pages, 3 figures
openalex publication_date 2014/09/19 · arxiv created 2015/09/02 · arxiv updated 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppäläinen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. We have analogous results out of equilibrium as well as for the middle point of the polymer with both ends fixed. The existence and the identification of the limit relies on the analysis of a random walk seen from its infimum.