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Predecessors in a random mapping

✍ Scribed by Jerzy Jaworski

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 208 KB
Volume: 13
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199810/12)13:3/4<501::aid-rsa17>3.0.co;2-0

No coin nor oath required. For personal study only.

✦ Synopsis

A random mapping T ; q of a finite set V, V s 1, 2, . . . , n into itself assigns independently to each i g V its unique image j g V with probability q if i s j and with Ž . Ž . probability Ps 1 y q r n y 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 Ž . inverse epidemic process on a random digraph G representing T ; q .

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