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Poisson Convergence in the n-Cube

✍ Scribed by Karl Weber

Publisher: John Wiley and Sons
Year: 1987
Tongue: English
Weight: 426 KB
Volume: 131
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19871310105

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✦ Synopsis

We consider two types of random subgraphs of the n-cube Q, obtained by independent deletion the vertices (together with all edges incident with them) or the edges of Q,,, respectively, with a prescribed probability q = 1p . For these two probabilistic models we determine some values of the probability p for which the number of (isolated) L-dimensional subcubes or the number of vertices of a given degree k, respectively, has asymptotically a Poisson or a Normal distribntion. The technique which will he wed is that of Poisson convergence introduced by

BARBOUR [I] (see also [a]).

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