Meeting and coalescence times for random walks in the largest component of the Erd\H{o}s-R\'enyi random graph

Vyacheslav Koval; Yuval Peres; Pieter Trapman

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arXiv · 2607.13183

Meeting and coalescence times for random walks in the largest component of the Erd\H{o}s-R\'enyi random graph

Vyacheslav Koval·Yuval Peres·Pieter Trapman

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Abstract

We prove that the stationary and worst-case expected meeting times of two independent continuous-time random walks on the largest component of the Erd\H{o}s-R\'enyi random graph $G(n,p)$ have order $n$ throughout the strictly supercritical, the slightly supercritical and the critical regimes. Using these bounds along with a fine-tuned combination of comparison inequalities due to Oliveira (2012) and Kanade-Mallmann-Trenn-Sauerwald (KMS, 2023), we deduce that expected coalescence time and full voter-model consensus also have order $n$ throughout these three regimes.

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Vyacheslav Koval, Yuval Peres, Pieter Trapman. 2026-07-14. Meeting and coalescence times for random walks in the largest component of the Erd\H{o}s-R\'enyi random graph. https://arxiv.org/abs/2607.13183

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