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Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder

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  • Clark, Jeremy
  • Lochridge, Casey

Abstract

We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we prove a distributional limit theorem for the partition function in a limiting regime wherein the system grows as the coupling of the polymer to the random environment is appropriately attenuated. The sequence of diamond graphs is determined by a choice of a branching number b∈{2,3,…} and segmenting number s∈{2,3,…}, and our focus is on the critical case of the model where b=s. This extends recent work in the critical case of analogous models with disorder variables placed at the edges of the graphs rather than the vertices.

Suggested Citation

  • Clark, Jeremy & Lochridge, Casey, 2023. "Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 75-102.
    • Handle: RePEc:eee:spapps:v:158:y:2023:i:c:p:75-102
    DOI: 10.1016/j.spa.2022.12.014
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    References listed on IDEAS

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    1. Alberts, Tom & Clark, Jeremy & Kocić, Saša, 2017. "The intermediate disorder regime for a directed polymer model on a hierarchical lattice," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3291-3330.
    2. Clark, Jeremy Thane, 2020. "Continuum directed random polymers on disordered hierarchical diamond lattices," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1643-1668.
    3. Lacoin, Hubert & Moreno, Gregorio, 2010. "Directed polymers on hierarchical lattices with site disorder," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 467-493, April.
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    Cited by:

    1. Keçoğlu, Ibrahim & Berker, A. Nihat, 2023. "Global Ashkin–Teller phase diagrams in two and three dimensions: Multicritical bifurcation versus double tricriticality—endpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Pektaş, Yiğit Ertaç & Artun, E. Can & Berker, A. Nihat, 2023. "Driven and non-driven surface chaos in spin-glass sponges," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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