{"title":"Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs","authors":"A. V. Nadutkina, A. N. Tikhomirov, D. A. Timushev","doi":"10.1134/s1055134424020056","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the spectra of random weighted bipartite graphs. We establish that, under\nspecific assumptions on the edge probabilities, the symmetrized empirical spectral distribution\nfunction of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur\ndistribution function.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"2012 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424020056","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the spectra of random weighted bipartite graphs. We establish that, under
specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution
function of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur
distribution function.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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