Start with a system of particles with possibly different masses, and consider a process where the particles merge, as time passes, according to some random mechanism. At some point of time the identity of the most massive particle–the leader–becomes fixed. We study the fixation time of the identity of the leader in the general setting of Aldous’s multiplicative coalescent, which in an asymptotic sense describes the evolution of the component sizes of a wide array of near-critical coalescent processes, including the classical Erdos-Renyi process. In particular, this generalizes a result of Luczak. Based on joint work with Louigi Addario-Berry and Shankar Bhamidi.

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Last updated: 18 May 2024