2010/12/21 by Francesco Caravenna, Caravenna, Francesco, Philippe Carmona +3
Mathematics · Physics and Astronomy · #60K37 #82B41 #82B44 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K37 #msc:82B41 #msc:82B44
paper · pdf · doi:10.48550/arxiv.1012.4653
32 pages
arxiv created 2010/12/21 · openalex publication_date 2010/12/21 · arxiv updated 2010/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+d)-dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the d orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows ballistically. We give an explicit characterization of the localization point and of the typical paths of the model.