{"title":"Predecessors in a random mapping","authors":"J. Jaworski","doi":"10.1002/(SICI)1098-2418(199810/12)13:3/4%3C501::AID-RSA17%3E3.0.CO;2-0","DOIUrl":null,"url":null,"abstract":"Ž . 4 ABSTRACT: A random mapping T ; q of a finite set V, Vs 1, 2, . . . , n into itself assigns independently to each igV its unique image jgV with probability q if is j and with Ž . Ž . probability Ps 1yq r ny1 if i/ j. The number of predecessors of elements from a given subset of V is studied. Exact results and limit theorems for the distribution of this random variable, the quasi-binomial distribution, are given. The results are applied to an Ž . inverse epidemic process on a random digraph G representing T ; q . Q 1998 John Wiley & T Sons, Inc. Random Struct. Alg., 13, 501]519, 1998","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/(SICI)1098-2418(199810/12)13:3/4%3C501::AID-RSA17%3E3.0.CO;2-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18
Abstract
Ž . 4 ABSTRACT: A random mapping T ; q of a finite set V, Vs 1, 2, . . . , n into itself assigns independently to each igV its unique image jgV with probability q if is j and with Ž . Ž . probability Ps 1yq r ny1 if i/ j. The number of predecessors of elements from a given subset of V is studied. Exact results and limit theorems for the distribution of this random variable, the quasi-binomial distribution, are given. The results are applied to an Ž . inverse epidemic process on a random digraph G representing T ; q . Q 1998 John Wiley & T Sons, Inc. Random Struct. Alg., 13, 501]519, 1998
Ž。摘要:随机映射T;有限集合V, V 1,2，…的q。， n into自身独立地为每个igV分配其唯一的图像jgV，其概率为q，如果为j，则为Ž。Ž。如果i/ j，则概率为p 1yq r ny1。研究了给定V子集中元素的前导个数。给出了拟二项分布的精确结果和极限定理。结果应用于Ž。表示T的随机有向图G上的逆流行过程;q。1998 John Wiley & T Sons, Inc.;随机结构。Alg。[j] .农业科学，1998,18 (2):1 - 5
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