Brownian excursions, critical random graphs and the multiplicative coalescent
Open Access
- 1 April 1997
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 25 (2) , 812-854
- https://doi.org/10.1214/aop/1024404421
Abstract
Let (Bt(s); 0 s ! 1) be reflecting inhomogeneous Brownian motionwith drift t \Gamma s at time s, started with Bt(0) = 0. Consider therandom graph G(n; n\Gamma1+tn\Gamma4=3), whose largest components have sizeof order n2=3. Normalizing by n\Gamma2=3, the asymptotic joint distributionof component sizes is the same as the joint distribution of excursionlengths of Bt(Corollary 2). The dynamics of merging of componentsas t increases are abstracted to define the...Keywords
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