Geodesic
Asymptotic equipartition properties for simple hierarchical and networked structures
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 114-138 Cet article a éte moissonné depuis la source Numdam

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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.

DOI : 10.1051/ps/2010016
Classification : 4A15, 94A24, 60F10, 05C80
Keywords: asymptotic equipartition property, large deviation principle, relative entropy, random graph, multitype Galton-Watson tree, randomly coloured random graph, typed graph, typed tree 
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     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 = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2010016/}
}
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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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