{"title":"再看随机锥体的阈值现象","authors":"D. Hug, R. Schneider","doi":"10.1556/012.2021.01513","DOIUrl":null,"url":null,"abstract":"In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Another Look at Threshold Phenomena for Random Cones\",\"authors\":\"D. Hug, R. Schneider\",\"doi\":\"10.1556/012.2021.01513\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-03-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1556/012.2021.01513\",\"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/10.1556/012.2021.01513","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Another Look at Threshold Phenomena for Random Cones
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.