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 property, large deviation principle, relative entropy, random graph, multitype Galton-Watson tree, randomly coloured random graph, typed graph, typed tree
@article{PS_2012__16__114_0,
author = {Doku-Amponsah, Kwabena},
title = {Asymptotic equipartition properties for simple hierarchical and networked structures},
journal = {ESAIM: Probability and Statistics},
pages = {114--138},
year = {2012},
publisher = {EDP Sciences},
volume = {16},
doi = {10.1051/ps/2010016},
mrnumber = {2946123},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2010016/}
}
TY - JOUR AU - Doku-Amponsah, Kwabena TI - Asymptotic equipartition properties for simple hierarchical and networked structures JO - ESAIM: Probability and Statistics PY - 2012 SP - 114 EP - 138 VL - 16 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2010016/ DO - 10.1051/ps/2010016 LA - en ID - PS_2012__16__114_0 ER -
%0 Journal Article %A Doku-Amponsah, Kwabena %T Asymptotic equipartition properties for simple hierarchical and networked structures %J ESAIM: Probability and Statistics %D 2012 %P 114-138 %V 16 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2010016/ %R 10.1051/ps/2010016 %G en %F PS_2012__16__114_0
Doku-Amponsah, Kwabena. Asymptotic equipartition properties for simple hierarchical and networked structures. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 114-138. doi: 10.1051/ps/2010016
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