{"title":"具有中观延迟的网络演化","authors":"Sayan Banerjee, Shankar Bhamidi, Partha Dey, Akshay Sakanaveeti","doi":"arxiv-2409.10307","DOIUrl":null,"url":null,"abstract":"Fueled by the influence of real-world networks both in science and society,\nnumerous mathematical models have been developed to understand the structure\nand evolution of these systems, particularly in a temporal context. Recent\nadvancements in fields like distributed cyber-security and social networks have\nspurred the creation of probabilistic models of evolution, where individuals\nmake decisions based on only partial information about the network's current\nstate. This paper seeks to explore models that incorporate \\emph{network\ndelay}, where new participants receive information from a time-lagged snapshot\nof the system. In the context of mesoscopic network delays, we develop\nprobabilistic tools built on stochastic approximation to understand asymptotics\nof both local functionals, such as local neighborhoods and degree\ndistributions, as well as global properties, such as the evolution of the\ndegree of the network's initial founder. A companion paper explores the regime\nof macroscopic delays in the evolution of the network.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Network evolution with mesoscopic delay\",\"authors\":\"Sayan Banerjee, Shankar Bhamidi, Partha Dey, Akshay Sakanaveeti\",\"doi\":\"arxiv-2409.10307\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Fueled by the influence of real-world networks both in science and society,\\nnumerous mathematical models have been developed to understand the structure\\nand evolution of these systems, particularly in a temporal context. Recent\\nadvancements in fields like distributed cyber-security and social networks have\\nspurred the creation of probabilistic models of evolution, where individuals\\nmake decisions based on only partial information about the network's current\\nstate. This paper seeks to explore models that incorporate \\\\emph{network\\ndelay}, where new participants receive information from a time-lagged snapshot\\nof the system. In the context of mesoscopic network delays, we develop\\nprobabilistic tools built on stochastic approximation to understand asymptotics\\nof both local functionals, such as local neighborhoods and degree\\ndistributions, as well as global properties, such as the evolution of the\\ndegree of the network's initial founder. A companion paper explores the regime\\nof macroscopic delays in the evolution of the network.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10307\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10307","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Fueled by the influence of real-world networks both in science and society,
numerous mathematical models have been developed to understand the structure
and evolution of these systems, particularly in a temporal context. Recent
advancements in fields like distributed cyber-security and social networks have
spurred the creation of probabilistic models of evolution, where individuals
make decisions based on only partial information about the network's current
state. This paper seeks to explore models that incorporate \emph{network
delay}, where new participants receive information from a time-lagged snapshot
of the system. In the context of mesoscopic network delays, we develop
probabilistic tools built on stochastic approximation to understand asymptotics
of both local functionals, such as local neighborhoods and degree
distributions, as well as global properties, such as the evolution of the
degree of the network's initial founder. A companion paper explores the regime
of macroscopic delays in the evolution of the network.