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arXiv · 1802.03834

Continuum directed random polymers on disordered hierarchical diamond lattices

Jeremy Clark
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Abstract

I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the \textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving pathways. This fractal depends on a branching parameter $b\in \mathbb{N}$ and a segmenting number $s\in \mathbb{N}$. 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, Khanin, Quastel [Journal of Statistical Physics \textbf{154}, 305-326 (2014)].

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Jeremy Clark. 2018-02-11. Continuum directed random polymers on disordered hierarchical diamond lattices. https://doi.org/10.1016/j.spa.2019.05.008

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