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math.PR2019★ 1 cited
The conditional Gaussian multiplicative chaos structure underlying a critical continuum random polymer model on a diamond fractal
Jeremy T. Clark
We discuss a Gaussian multiplicative chaos (GMC) structure underlying a family of random measures , indexed by , on a space of directed pathways c…
math.PR2018
Continuum directed random polymers on disordered hierarchical diamond lattices
Jeremy Clark
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 sel…
math.PR2017
High-temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder
Jeremy Clark
Diamond "lattices" are sequences of recursively-defined graphs that provide a network of directed pathways between two fixed root nodes, and . The construction recipe for di…