  We study a point process describing the asymptotic behavior of sizes of the
largest components of the random graph G(n,p) in the critical window
p=n^{-1}+lambda n^{-4/3}. In particular, we show that this point process has a
surprising rigidity. Fluctuations in the large values will be balanced by
opposite fluctuations in the small values such that the sum of the values
larger than a small epsilon is almost constant.
