Abstract
We give a short proof that the largest component C 1 of the random graph G(n, 1/n) is of size approximately n 2/3. The proof gives explicit bounds for the probability that the ratio is very large or very small. In particular, the probability that n −2/3|C 1| exceeds A is at most \({e^{ - c{A^3}}}\) for some c > 0.
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U.C. Berkeley and Microsoft Research. Research of both authors supported in part by NSF grants #DMS-0244479 and #DMS-0104073.
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Nachmias, A., Peres, Y. The critical random graph, with martingales. Isr. J. Math. 176, 29–41 (2010). https://doi.org/10.1007/s11856-010-0019-8
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DOI: https://doi.org/10.1007/s11856-010-0019-8