| Issue |
ESAIM: PS
Volume 16, 2012
|
|
|---|---|---|
| Page(s) | 114 - 138 | |
| DOI | https://doi.org/10.1051/ps/2010016 | |
| Published online | 03 July 2012 | |
Asymptotic equipartition properties for simple hierarchical and networked structures
Statistics Department, University of Ghana, Box LG 115, Legon, Ghana
kdoku@ug.edu.gh
Received: 19 June 2009
Revised: 31 March 2010
Revised: 9 June 2010
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.
Mathematics Subject Classification: 4A15 / 94A24 / 60F10 / 05C80
Key words: Asymptotic equipartition property / large deviation principle / relative entropy / random graph / multitype Galton-Watson tree / randomly coloured random graph / typed graph / typed tree.
© EDP Sciences, SMAI, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.