The maximum of the two dimensional Gaussian directed polymer in the subcritical regime

2025/03/21 by Clément Cosco, Cosco, Clément, Shuta Nakajima +3 · 2 citations
Mathematics · #82A51 #82D30 #FOS: Mathematics #Geometry and complex manifolds #Primary 60K37 #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #secondary 60K35

paper · pdf · doi:10.48550/arxiv.2503.17236

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the maximum ϕ_N^* of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an √ N × √ N box. We show that ϕ_N^*/log N converges towards a constant σ^*, which we identify to be the same as for the maximum of a branching random walk with a slowly varying variance profile as studied in Fang-Zeitouni, J. Stat. Phys. 2012 and (in the context of the generalized random energy model) in Bovier-Kurkova, Ann. Inst. H. Poincare 2004.

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