ASYMPTOTIC EQUIPARTITION PROPERTIES FOR SIMPLE HIERARCHICAL AND NETWORKED STRUCTURES

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 x n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical measures.