相关随机图的匹配恢复阈值

IF 3.2 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Statistics Pub Date : 2023-08-01 DOI:10.1214/23-aos2305

Jian Ding, Hang Du

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引用次数: 13

摘要

对于从一个公共Erdős-Rényi图G(n,p)中独立子采样的两个相关图，我们希望从这两个没有标记的图的观察中恢复它们的潜在顶点匹配。对于α∈(0,1)，当p=n−α+o(1)时，我们建立了一个尖锐的信息论阈值，以确定是否有可能正确匹配顶点的正分数。我们的结果强化了Wu, Xu和Yu最近工作中的一个常数因素。

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Matching recovery threshold for correlated random graphs

For two correlated graphs which are independently sub-sampled from a common Erdős–Rényi graph G(n,p), we wish to recover their latent vertex matching from the observation of these two graphs without labels. When p=n−α+o(1) for α∈(0,1], we establish a sharp information-theoretic threshold for whether it is possible to correctly match a positive fraction of vertices. Our result sharpens a constant factor in a recent work by Wu, Xu and Yu.

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来源期刊

Annals of Statistics 数学-统计学与概率论

CiteScore

9.30

自引率

8.90%

发文量

119

审稿时长

6-12 weeks

期刊介绍： The Annals of Statistics aim to publish research papers of highest quality reflecting the many facets of contemporary statistics. Primary emphasis is placed on importance and originality, not on formalism. The journal aims to cover all areas of statistics, especially mathematical statistics and applied & interdisciplinary statistics. Of course many of the best papers will touch on more than one of these general areas, because the discipline of statistics has deep roots in mathematics, and in substantive scientific fields.