This is the critical step of the proof. Originally it was dealt with by means of Janson's inequality, a type of concentration inequality for multivariate polynomials. Tao & Vu (2006)Section 1.8 of Tao & Vu (2006). present this proof with a more sophisticated two-sided concentration inequality by V. Vu (2000), thus relatively simplifying this step. Alon & Spencer (2016) classify this proof as an instance of the Poisson paradigm.Chapter 8, p. 139 of Alon & Spencer (2016).
