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Predecessors in a random mapping
Author(s) -
Jaworski Jerzy
Publication year - 1998
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199810/12)13:3/4<501::aid-rsa17>3.0.co;2-0
Subject(s) - mathematics , combinatorics , digraph , random variable , struct , binomial (polynomial) , limit (mathematics) , discrete mathematics , distribution (mathematics) , binomial distribution , inverse , statistics , computer science , mathematical analysis , geometry , programming language
A random mapping ( T ; q ) of a finite set V , V ={1, 2,…, n } into itself assigns independently to each i ∈ V its unique image j ∈ V with probability q if i = j and with probability P =(1− q )/( n −1) 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 inverse epidemic process on a random digraph G T representing ( T ; q ). © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 501–519, 1998
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