A point process describing the component sizes in the critical window of the random graph evolution
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
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.
IdentifiersURN: urn:nbn:se:uu:diva-26316DOI: 10.1017/S0963548306008327ISI: 000247845900007OAI: oai:DiVA.org:uu-26316DiVA: diva2:54090