Fluctuations of partition functions of directed polymers in weak disorder beyond the L²-phase

2022/02/07 by Stefan Junk, Junk, Stefan
Computer Science · Mathematics · Physics and Astronomy · #60K37 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2202.02907

openalex publication_date 2022/02/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We study the directed polymer model in a bounded environment in weak disorder but without L²-boundedness, specifically the speed of homogenization for the field (W_n^0,x)_{x∈\mathbb Z^d}, where W_n^0,x denotes the associated martingale for the polymer starting from x. We show that a suitably re-centered spatial average over a set of diameter n^1/2 convergence to zero at rate n^-ξ+o(1), where the exponent is an explicit function of the inverse temperature β.

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• Positive and negative moments for directed polymers in random environment in weak disorder
• The tail distribution of the partition function for directed polymer in the weak disorder phase
• Strong disorder and very strong disorder are equivalent for directed polymers
• The localization transition for the directed polymer in a random environment is smooth