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- W3120707093 abstract "We consider the near-critical ErdH{o}s-R'{e}nyi random graph $G(n,p)$ and provide a new probabilistic proof of the fact that, when $p$ is of the form $p=p(n)=1/n+lambda/n^{4/3}$ and $A$ is large, [mathbb{P}(|mathcal{C}_{max}|>An^{2/3})asymp A^{-3/2}e^{-frac{A^3}{8}+frac{lambda A^2}{2}-frac{lambda^2A}{2}}] where $mathcal{C}_{max}$ is the largest connected component of the graph. Our result allows $A$ and $lambda$ to depend on $n$. While this result is already known, our proof relies only on conceptual and adaptable tools such as ballot theorems, whereas the existing proof relies on a combinatorial formula specific to ErdH{o}s-R'{e}nyi graphs, together with analytic estimates." @default.
- W3120707093 created "2021-01-18" @default.
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- W3120707093 date "2021-01-13" @default.
- W3120707093 modified "2023-09-27" @default.
- W3120707093 title "Unusually large components in near-critical ErdH{o}s-R'{e}nyi graphs via ballot theorems" @default.
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