报告人：黄瀚（密苏里大学）

报告题目：Reconstructing the Geometry of Random Geometric Graphs

报告摘要：Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the manifold assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distances. (Joint work with P. Jiradilok and E. Mossel).

报告时间：2025年4月10日（星期四）10:00-12:00

报告地点：东三十一楼119会议室

邀请人：张宁

报告人简介：黄瀚，密苏里大学教授，高维概率和凸几何方向专家，其主要工作涵盖随机矩阵、随机图等方向，其工作发表于J. Euro. Math.、JFA、Prob. T. & Rel. Field等顶级期刊上。