{"title":"不可还原复反射群上 Cayley 图的电阻直径和临界概率","authors":"Maksim Vaskouski, Hanna Zadarazhniuk","doi":"10.1007/s10801-024-01302-5","DOIUrl":null,"url":null,"abstract":"<p>We consider networks on minimal Cayley graphs of irreducible complex reflection groups <i>G</i>(<i>m</i>, <i>p</i>, <i>n</i>). We show that resistance diameters of these graphs have asymptotic <span>\\(\\Theta (1/n)\\)</span> as <span>\\(n\\rightarrow \\infty \\)</span> under fixed <i>m</i>, <i>p</i>. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups\",\"authors\":\"Maksim Vaskouski, Hanna Zadarazhniuk\",\"doi\":\"10.1007/s10801-024-01302-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider networks on minimal Cayley graphs of irreducible complex reflection groups <i>G</i>(<i>m</i>, <i>p</i>, <i>n</i>). We show that resistance diameters of these graphs have asymptotic <span>\\\\(\\\\Theta (1/n)\\\\)</span> as <span>\\\\(n\\\\rightarrow \\\\infty \\\\)</span> under fixed <i>m</i>, <i>p</i>. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-024-01302-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-024-01302-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Resistance diameters and critical probabilities of Cayley graphs on irreducible complex reflection groups
We consider networks on minimal Cayley graphs of irreducible complex reflection groups G(m, p, n). We show that resistance diameters of these graphs have asymptotic \(\Theta (1/n)\) as \(n\rightarrow \infty \) under fixed m, p. Non-trivial lower and upper asymptotic bounds for critical probabilities of percolation for there appearing a giant connected component have been obtained.
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