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Large deviations for the degree structure in preferential attachment schemes. (English) Zbl 1273.60031

A preferential attachment scheme is specified with two functions of time: a probability \(p(t)\) and a non-negative weight component \(b(t)\). At each time step \(t\) a new node is attached to the current graph. With probability \(p(t)\) it is attached as an isolated node, and with probability \(1-p(t)\) it is attached by an edge to a node in the current graph that is selected with probability proportional to a weight \(w(t,d)=d+b(t)\) of its degree \(d\) and time \(t\). Using this scheme the convergence to power law distributions and other laws are investigated for the empirical degree distribution.

MSC:

60F10 Large deviations
05C80 Random graphs (graph-theoretic aspects)
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