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- W4287758848 abstract "In the Reed-Frost model, an example of an SIR epidemic model, one can examine a statistic that counts the number of concurrently infected individuals. This statistic can be reformulated as a statistic on the ER random graph $G(n,p)$. Within the critical window of Aldous and Martin-L{o}f, i.e. when $p = p(n) = n^{-1}+lambda n^{-4/3}$, the cumulative sum of this statistic converges weakly to the integral of a Brownian motion with parabolic drift. This same statistic exhibits a deterministic scaling limit when $p = (1+lambda varepsilon_n)/n$ whenever $varepsilon_nto 0$ and $n^{1/3}varepsilon_ntoinfty$." @default.
- W4287758848 created "2022-07-26" @default.
- W4287758848 creator A5065741387 @default.
- W4287758848 date "2020-06-11" @default.
- W4287758848 modified "2023-09-26" @default.
- W4287758848 title "A new relationship between ErdH{o}s-R'{e}nyi graphs, epidemic models and Brownian motion with parabolic drift" @default.
- W4287758848 doi "https://doi.org/10.48550/arxiv.2006.06838" @default.
- W4287758848 hasPublicationYear "2020" @default.
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