Directed polymers in a random environment: A review of the phase transitions

Nikos Zygouras

Stochastic Processes and their Applications, 2024, vol. 177, issue C

Abstract: The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to novel statistical behaviours. Despite its intense study, there are still many aspects and phases which have not yet been identified. In this review we focus on the current status of our understanding of the transition between weak and strong disorder phases, give an account of some of the methods that the study of the model has motivated and highlight some open questions.

Keywords: Random polymers; Disordered systems; Phase transitions; Weak and strong disorder; Martingales; Fractional moment method; Coarse graining; Pinning models; Heavy tail disorder; Hierarchical lattices; Intermediate disorder regime (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104431

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