On the Brownian directed polymer in a Gaussian random environment

2004/09/08 by Carles Rovira, Rovira, Carles, amy Tindel +1
Mathematics · #60H07 #60K37 #82D60 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60H07 #msc:60K37 #msc:82D60

paper · pdf · doi:10.48550/arxiv.math/0409135

arxiv created 2004/09/08 · openalex publication_date 2004/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.

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