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Large Deviations of the Degree Structure in Preferential Attachment Schemes | | Jihyeok Choi And Sunder Sethuraman
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30 May 2011 | | Abstract: | Preferential attachment schemes where the selection mechanism is possibly
time-dependent are considered, and an infinite dimensional large deviation
principle for the sample path evolution of the empirical degree distribution is
found by Dupuis-Ellis type methods. Interestingly, the rate function, which can
be evaluated, includes a term which accounts for the cost of assigning a
fraction of the total degree to an ’infinite’ degree component. As a
consequence of the large deviation results, a sample path a.s. law of large
numbers for the degree structure is deduced in terms of a coupled system of
ODE’s from which power law bounds for the limiting degree distribution are
given. However, by analyzing the rate function, one can see that the process
can deviate to a variety of non-power law distributions with finite cost. | | Source: | arXiv, 1105.6047 | | Services: | Forum | Review | PDF | Favorites | |
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