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Continuum directed random polymers on disordered hierarchical diamond lattices

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  • Clark, Jeremy Thane

Abstract

I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the diamond hierarchical lattice, a self-similar metric space forming a network of interweaving pathways. This fractal depends on a branching parameter b∈N and a segmenting number s∈N. For s>b my focus is on random measures on the set of directed paths that can be formulated as a subcritical Gaussian multiplicative chaos. This path measure is analogous to the continuum directed random polymer introduced by Alberts et al. (2014).

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  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1643-1668
    DOI: 10.1016/j.spa.2019.05.008
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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. 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. 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.

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