## Seminars

## Seminars

## Probability and Statistics Seminar——Shotgun threshold for sparse Erdős-Rényi graphs

**Holder：** Heng Ma (Peking University)

**Time：**2023-02-20 14:00-15:00

**Location：**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，北京大学2020级博士生, 导师为任艳霞教授。

**Your participation is warmly welcomed! **