# Moderate deviations of subgraph counts in the Erdős-Rényi random graphs $G(n,m)$ and $G(n,p)$

Goldschmidt, C
Griffiths, S
SCOTT, A

## Journal:

Transactions of the American Mathematical Society

## Last Updated:

2020-10-10T17:39:59.29+01:00

## abstract:

rate associated with moderate deviations of subgraph counts in the
Erd\H{o}s-R\'enyi random graph $G(n,m)$. Our approach is based on applying Freedman's inequalities for the probability of deviations of martingales to a martingale representation of subgraph count deviations. In addition, we prove that subgraph count deviations of different subgraphs are all linked, via the deviations of two specific graphs, the path of length two and the triangle. We also deduce new bounds for the related $G(n,p)$ model.

976067

Submitted

Journal Article