AI 中文总结
研究厄多斯-雷尼随机图最大连通分量上随机游走的相遇和合并时间，通过证明相遇时间界限并结合比较不等式，得出预期合并时间和完全选民模型共识在严格超临界、轻微超临界和临界区域都为\(n\)阶。
AI 中文摘要
我们证明了在厄多斯-雷尼随机图\(G(n,p)\)的最大连通分量上，两个独立连续时间随机游走的平稳和最坏情况预期相遇时间在严格超临界、轻微超临界和临界区域都具有\(n\)阶。利用这些界限以及Oliveira（2012）和Kanade-Mallmann-Trenn-Sauerwald（KMS，2023）的比较不等式的微调组合，我们推断出在这三个区域中预期合并时间和完全选民模型共识也具有\(n\)阶。
英文摘要
We prove that the stationary and worst-case expected meeting times of two independent continuous-time random walks on the largest component of the Erdős-Rényi 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.
