在各向异性随机几何图中检测高维几何的阈值

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2023-08-01 DOI:10.1002/rsa.21178

Matthew Brennan, Guy Bresler, Brice Huang

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引用次数: 1

摘要

在各向异性随机几何图模型中，顶点对应于从高维高斯分布中绘制的点，如果两个顶点的距离小于指定的阈值，则两个顶点相连。我们研究了在这种图和具有相同边概率的Erdős‐rsamnyi图之间何时可能进行假设检验。它是顶点的数目，是特征值的向量，Eldan和Mikulincer, Geo。函数方面。分析:以色列研讨会，2017年表明，检测何时可能，何时不可能。我们表明，当缩小这一差距并肯定地解决Eldan和Mikulincer, Geo的猜想时，检测是不可能的。函数方面。分析:以色列研讨会，2017。

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Threshold for detecting high dimensional geometry in anisotropic random geometric graphs

Abstract In the anisotropic random geometric graph model, vertices correspond to points drawn from a high‐dimensional Gaussian distribution and two vertices are connected if their distance is smaller than a specified threshold. We study when it is possible to hypothesis test between such a graph and an Erdős‐Rényi graph with the same edge probability. If is the number of vertices and is the vector of eigenvalues, Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017 shows that detection is possible when and impossible when . We show detection is impossible when , closing this gap and affirmatively resolving the conjecture of Eldan and Mikulincer, Geo. Aspects Func. Analysis: Israel seminar, 2017.

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.