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

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  • Zygouras, Nikos

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.

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  • Zygouras, Nikos, 2024. "Directed polymers in a random environment: A review of the phase transitions," Stochastic Processes and their Applications, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:spapps:v:177:y:2024:i:c:s0304414924001376
    DOI: 10.1016/j.spa.2024.104431
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    References listed on IDEAS

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    4. Tom Alberts & Jeremy Clark, 2019. "Nested Critical Points for a Directed Polymer on a Disordered Diamond Lattice," Journal of Theoretical Probability, Springer, vol. 32(1), pages 64-89, March.
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    7. Cosco, Clément & Nakajima, Shuta & Nakashima, Makoto, 2022. "Law of large numbers and fluctuations in the sub-critical and L2 regions for SHE and KPZ equation in dimension d≥3," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 127-173.
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