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arXiv · 1610.01281

A Quantitative Local Limit Theorem for Triangles in Random Graphs

Ross Berkowitz
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Abstract

In this paper we prove a quantiative local limit theorem for the distribution of the number of triangles in the Erdős-Renyi random graph $G(n,p)$, for a fixed $p\in (0,1)$. This proof is an extension of the previous work of Gilmer and Kopparty, who proved that the local limit theorem held asymptotically for triangles. Our work gives bounds on the $\ell^1$ and $\ell^\infty$ distance of the triangle distribution from a suitable discrete normal.

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Ross Berkowitz. 2017-03-21. A Quantitative Local Limit Theorem for Triangles in Random Graphs. https://arxiv.org/abs/1610.01281

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