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• W2982521868 abstract "We analyse the scaling limit of the sizes of the largest components of the Random Intersection Graph $G(n,m,p)$ close to the critical point $p=frac{1}{sqrt{nm}}$, when the numbers $n$ of individuals and $m$ of communities have different orders of magnitude. We find out that if $m gg n$, then the scaling limit is identical to the one of the ER Random Graph (ERRG), while if $n gg m$ the critical exponent is similar to that of Inhomogeneous Random Graphs with heavy-tailed degree distributions, yet the rescaled component sizes have the same limit in distribution as in the ERRG. This suggests the existence of a wide universality class of inhomogeneous random graph models such that in the critical window the largest components have sizes of order $n^{rho}$ for some $rho in (1/2,2/3]$, which depends on some parameter of the graph." @default.
• W2982521868 created "2019-11-08" @default.
• W2982521868 creator A5046071788 @default.
• W2982521868 date "2019-10-29" @default.
• W2982521868 modified "2023-09-27" @default.
• W2982521868 title "Critical scaling limits of the random intersection graph" @default.
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• W2982521868 hasPublicationYear "2019" @default.
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