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 - https://www.scopus.com/pages/publications/77953481974
U2 - 10.1007/s11856-010-0019-8
DO - 10.1007/s11856-010-0019-8
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -