Hipster random walks
Probability
2019-09-17 v1 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.1909.07367,
title = {Hipster random walks},
author = {Louigi Addario-Berry and Hannah Cairns and Luc Devroye and Celine Kerriou and Rivka Mitchell},
journal= {arXiv preprint arXiv:1909.07367},
year = {2019}
}
Comments
28 pages