On the Central Limit Theorem for the log-partition function of 2D directed polymers

2024/02/22 by Cosco, Clément, Donadini, Anna · 1 citation
#60G50 #82B44 #FOS: Mathematics #Primary: 60F05 #Probability (math.PR) #Secondary: 82D60

paper · doi:10.48550/arxiv.2402.14647

Abstract

The log-partition function log W_N(β) of the two-dimensional directed polymer in random environment is known to converge in distribution to a normal distribution when considering temperature in the subcritical regime β=β_N=β√(π/log N), β∈ (0,1) (Caravenna, Sun, Zygouras, Ann. Appl. Prob. (2017)). In this paper, we present an elementary proof of this result relying on a decoupling argument and the central limit theorem for sums of independent random variables. The argument is inspired by an analogy of the model to branching random walks.

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