Continuum directed random polymers on disordered hierarchical diamond lattices

Jeremy Thane Clark

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1643-1668

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).

Keywords: Gaussian multiplicative chaos; Diamond hierarchical lattice; Random branching graphs (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2019.05.008

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