# Anti-concentration for subgraph counts in random graphs

@article{Fox2019AnticoncentrationFS,
title={Anti-concentration for subgraph counts in random graphs},
author={Jacob Fox and Matthew Kwan and Lisa Sauermann},
journal={The Annals of Probability},
year={2019}
}
• Published 29 May 2019
• Mathematics
• The Annals of Probability
Fix a graph $H$ and some $p\in (0,1)$, and let $X_H$ be the number of copies of $H$ in a random graph $G(n,p)$. Random variables of this form have been intensively studied since the foundational work of Erdős and Renyi. There has been a great deal of progress over the years on the large-scale behaviour of $X_H$, but the more challenging problem of understanding the small-ball probabilities has remained poorly understood until now. More precisely, how likely can it be that $X_H$ falls in some…

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