Asymptotic diameter of preferential attachment model

YMSC Probability Seminar

Oragnizers：

吴昊，杨帆，姜建平，顾陈琳

Speaker：

Shuyang Gong 巩舒阳 (PKU)

Zhangsong Li 李章颂 (PKU)

Time：

Thur., 16:00-17:00, May 29, 2025

Venue：

C548, Shuangqing Complex Building A

Title：

Asymptotic diameter of preferential attachment model

Abstract:

We study the asymptotic diameter of the preferential attachment model $\PA_n^{(m,\delta)}$ with parameters $m \ge 2$ and $\delta > 0$. Building on the recent work [Hofstad and Zhu 25], we prove that the diameter of $G_n \sim \PA_n^{(m,\delta)}$ is $(1+o(1))\log_\nu n$ with high probability, where $\nu$ is the exponential growth rate of the local weak limit of $G_n$. Our result confirms the conjecture in [Hofstad and Zhu 25] and closes the remaining gap in understanding the asymptotic diameter of preferential attachment graphs with general parameters $m \ge 1$ and $\delta >-m$. Our proof follows a general recipe that relates the diameter of a random graph to its typical distance, which we expect to have applicability in a broader range of models. This talk is based on joint work with Hang Du (MIT) and Haodong Zhu (TUE).