Mittagsseminar (by J. Lengler, K. Bringmann, B. Gärtner, M. Hoffmann, R. Kyng, D.Steurer, V. Traub)

Date and Time: Tuesday, May 19, 2026, 12:15 pm

Duration: 30 minutes

Location: OAT S15

Speaker: Kostas Lakis

The Dispersion Process on Random Graphs

The Dispersion Process, introduced by Cooper et al. in 2018, proceeds as follows. Initially, M particles are placed on some origin vertex. The process then proceeds in rounds. In each round, every vertex with at least 2 particles on it topples, meaning every particle chooses a neighboring vertex to move to uniformly at random. When all vertices have at most 1 particle, the process terminates. In the clique with n vertices, there is a phase transition around M=n/2 particles, below and above which the process takes logarithmically and exponentially many rounds respectively. We show the same result for G(n, p) in the regime where the expected degrees are polynomial, i.e. the diameter of the graph is constant.

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