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Asymptotic equipartition properties for simple hierarchical and networked structures

Published online by Cambridge University Press:  03 July 2012

Kwabena Doku-Amponsah
Kwabena Doku-Amponsah*
Affiliation:
Statistics Department, University of Ghana, Box LG 115, Legon, Ghana. [email protected]
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Abstract

We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.

Keywords

Asymptotic equipartition propertylarge deviation principlerelative entropyrandom graphmultitype Galton-Watson treerandomly coloured random graphtyped graphtyped tree.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 114 - 138
Copyright
© EDP Sciences, SMAI, 2012

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References

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