We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent r satisfies r > 4. We see that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, extending results of [1]. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme to study the critical behavior in inhomogeneous random graphs of so-called rank-1 initiated in [12].

Original language | English |
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Publisher | s.n. |
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Number of pages | 19 |
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Publication status | Published - 2009 |
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Name | arXiv.org [math.PR] |
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Volume | 0907.4279 |
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