TY - JOUR

T1 - The critical random graph, with martingales

AU - Nachmias, Asaf

AU - Peres, Yuval

N1 - Funding Information:
∗U.C. Berkeley and Microsoft Research. Research of both authors part by NSF grants #DMS-0244479 and #DMS-0104073. Received February 3, 2006 and in revised form August 2, 2007

PY - 2010/3

Y1 - 2010/3

N2 - We give a short proof that the largest component C1 of the random graph G(n, 1/n) is of size approximately n2/3. 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{pipe}C1{pipe} exceeds A is at most e-cA^3 for some c > 0.

AB - We give a short proof that the largest component C1 of the random graph G(n, 1/n) is of size approximately n2/3. 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{pipe}C1{pipe} exceeds A is at most e-cA^3 for some c > 0.

UR - http://www.scopus.com/inward/record.url?scp=77953481974&partnerID=8YFLogxK

U2 - 10.1007/s11856-010-0019-8

DO - 10.1007/s11856-010-0019-8

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AN - SCOPUS:77953481974

SN - 0021-2172

VL - 176

SP - 29

EP - 41

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -