We study noise sensitivity of properties of the largest components $(C_1,C_2,C_3,...)$ of the random graph $G(n,p)$ in its critical window $p=(1+\lambda n^{−1/3})/n$. For instance, are the properties “|C_1| exceeds its median” or “the diameter of C_2 exceeds its median” noise sensitive?
We show a dichotomy for noise sensitivity that coincides with the critical window: If the noise...