Hipster random walks, random series-parallel graph and random homogeneous systems
Probability
2026-04-13 v2
Abstract
We study a class of random homogeneous systems. Our main result says that under suitable general assumptions, these systems converge weakly, upon a suitable normalization, to the probability distribution with density . Two special cases are of particular interest: for the effective resistance of the critical random series-parallel graph, our result gives an affirmative answer to a conjecture of Hambly and Jordan (Adv. Appl. Probab. 2004) and further conjectures of Addario-Berry et al. (Probab.Theory Related Fields 2020) and Derrida whereas for the hipster random walk, we recover a previous result of Addario-Berry et al.~(Probab. Theory Related Fields 2020).
Cite
@article{arxiv.2511.16880,
title = {Hipster random walks, random series-parallel graph and random homogeneous systems},
author = {Xinxing Chen and Thomas Duquesne and Zhan Shi},
journal= {arXiv preprint arXiv:2511.16880},
year = {2026}
}