Probability and Statistics Seminar—— Shotgun threshold for sparse Erdős-Rényi graphs
报告人：Heng Ma (PKU)
时间：2023-02-20 14:00-15:00
地点：Room 1114, Sciences Building No. 1
Abstract: In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth $r$ (up to isomorphism) for some $r \geq 1$ and we wish to recover the underlying graph up to isomorphism. When the underlying graph is an Erdős-Rényi $\mathcal{G}\left(n, \frac{\lambda}{n}\right)$, we show that the shotgun assembly threshold $r_{*} \approx \frac{\log n}{\log \left(\lambda^{2} \gamma_{\lambda}\right)^{-1}}$ where $\gamma_{\lambda}$ is the probability for two independent Poisson-Galton-Watson trees with parameter $\lambda$ to be rooted isomorphic with each other. Our result sharpens a constant factor in a previous work by Mossel and Ross (2019) and thus solve a question therein. This talk is based on a joint work with Jian Ding and Yiyang Jiang.
About the Speaker:
马恒是英国威廉希尔公司2020级博士生，导师为任艳霞教授。
