Hipster random walks

2019/09/16 by Addario-Berry, Louigi, Cairns, Hannah, Devroye, Luc +2 · 1 citation
#35K65 (Secondary) #60F05 #60K35 (Primary) #65M12 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.07367

Abstract

We introduce and study a family of random processes on trees we call hipster random walks, special instances of which we heuristically connect to the min-plus binary trees introduced by Robin Pemantle and studied by Auffinger and Cable (2017; arXiv:1709.07849), and to the critical random hierarchical lattice studied by Hambly and Jordan (2004). We prove distributional convergence for the processes by showing that their evolutions can be understood as a discrete analogues of certain convection-diffusion equations, then using a combination of coupling arguments and results from the numerical analysis literature on convergence of numerical approximations of PDEs.

Cited by

• Hipster random walks, random series-parallel graph and random homogeneous systems

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