Random 0/1-polytopes sampled with constant probability p have edge-expansion Θ(n) for p > 1/2 and n^Θ(log log n) for p < 1/2 with high probability.
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Random 0/1-polytopes expand rapidly
Random 0/1-polytopes sampled with constant probability p have edge-expansion Θ(n) for p > 1/2 and n^Θ(log log n) for p < 1/2 with high probability.