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- W4297776127 abstract "We show that the random number $T_n$ of triangles in a random graph on $n$ vertices, with a strict constraint on the total number of edges, admits an expansion $T_n = an^3 + bn^2 + F_n$, where $a$ and $b$ are numbers, with the mean $langle F_n rangle = O(n)$ and the standard deviation $sigma(T_n) =sigma(F_n)= O(n^{3/2})$. The presence of a `surface term' $bn^2$ has a significance analogous to the macroscopic surface effects of materials, and is missing in the model where the edge constraint is removed. We also find the surface effect in other graph models using similar edge constraints." @default.
- W4297776127 created "2022-10-01" @default.
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- W4297776127 date "2017-09-04" @default.
- W4297776127 modified "2023-10-16" @default.
- W4297776127 title "Surface effects in dense random graphs with sharp edge constraint" @default.
- W4297776127 doi "https://doi.org/10.48550/arxiv.1709.01036" @default.
- W4297776127 hasPublicationYear "2017" @default.
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