随机双正则二部图的全局特征值波动

IF 0.9 4区数学 Q4 PHYSICS, MATHEMATICAL Random Matrices-Theory and Applications Pub Date : 2020-08-26 DOI:10.1142/s2010326323500041

Ioana Dumitriu, Yizhe Zhu

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引用次数: 5

摘要

我们计算了一类大解析函数的均匀分布的具有固定增长度的随机双正则二部图的特征值涨落。作为证明的关键步骤，我们获得了随机双正则二部图中循环和循环非回溯行走数的泊松近似的总变异距离界，这可能是独立的兴趣。作为一个应用，我们将结果转化为均匀分布随机正则超图的邻接矩阵。

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Global eigenvalue fluctuations of random biregular bipartite graphs

We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backtracking walks in random biregular bipartite graphs, which might be of independent interest. As an application, we translate the results to adjacency matrices of uniformly distributed random regular hypergraphs.

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来源期刊

Random Matrices-Theory and Applications Decision Sciences-Statistics, Probability and Uncertainty

CiteScore

1.90

自引率

11.10%

发文量

期刊介绍： Random Matrix Theory (RMT) has a long and rich history and has, especially in recent years, shown to have important applications in many diverse areas of mathematics, science, and engineering. The scope of RMT and its applications include the areas of classical analysis, probability theory, statistical analysis of big data, as well as connections to graph theory, number theory, representation theory, and many areas of mathematical physics. Applications of Random Matrix Theory continue to present themselves and new applications are welcome in this journal. Some examples are orthogonal polynomial theory, free probability, integrable systems, growth models, wireless communications, signal processing, numerical computing, complex networks, economics, statistical mechanics, and quantum theory. Special issues devoted to single topic of current interest will also be considered and published in this journal.