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

Jeremy Clark and Casey Lochridge

Stochastic Processes and their Applications, 2023, vol. 158, issue C, 75-102

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.

Keywords: Directed polymer in a random environment; Weak coupling limit; Critical scaling window; Diamond hierarchical graphs (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:158:y:2023:i:c:p:75-102

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DOI: 10.1016/j.spa.2022.12.014

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