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A point process describing the component sizes in the critical window of the random graph evolution
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 16, no 4, 631-658 p.Article in journal (Refereed) Published
Abstract [en]

We study a point process describing the asymptotic behaviour of sizes of the largest components of the random graph G(n, p) in the critical window, that is, for p = n−1 + λn−4/3, where λ is a fixed real number. In particular, we show that this point process has a surprising rigidity. Fluctuations in the large values will be balanced by opposite fluctuations in the small values such that the sum of the values larger than a small (a scaled version of the number of vertices in components of size greater than εn2/3) is almost constant.

Place, publisher, year, edition, pages
2007. Vol. 16, no 4, 631-658 p.
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URN: urn:nbn:se:uu:diva-26316DOI: 10.1017/S0963548306008327ISI: 000247845900007OAI: oai:DiVA.org:uu-26316DiVA: diva2:54090
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2011-01-31Bibliographically approved

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Janson, Svante
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