We study the connected components in critical percolation on the Hamming hypercube $\{ 0,1\}^m$. We show that their sizes rescaled by $2^{ -2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled by $2^{ -m/3}$ and the uniform measure, they converge in distribution with respect to the Gromov-Hausdorff-Prokhorov topology. The two corresponding limits are as in critical Erd\H{ o}s-R\'enyi graphs.
Categories: math.PR