Large deviation principle for the empirical degree measure of preferential attachment random graphs

2014/04/04 by K. Doku-Amponsah, F. O. Mettle, E. N. N. Nortey
Mathematics · #math.PR #msc:60F10 #msc:05C80

paper · pdf · doi:10.5539/ijsp.v4n1p76

published as International Journal of Statistics and Probability; Vol. 4, No. 1( 2015), pp.68-75 · 12 pages. arXiv admin note: substantial text overlap with arXiv:1312.1053

arxiv created 2014/04/04 · arxiv updated 2015/01/29

Abstract

We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of their degree. For a class of linear preferential attachment random graphs we find a large deviation principle (LDP) for the empirical degree measure. In the course of the prove this LDP we establish an LDP for the empirical degree and pair distribution see Theorem 2.3, of the fitness preferential attachment model of random graphs.

Citations

• Large deviations, Basic information theorem for fitness preferential attachment random networks