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Coagulation systems: From Particle Systems to Random Graphs

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We consider random systems of coagulating particles, motivated by combinatorial objects which show up in many-body systems. In the scaling limit, the coagulation system is described by a deterministic limit (PDE) equation, due to Flory, which undergoes a phase transition in finite time. On the other hand, in certain cases, the random system can be described exactly by a kind of random graph, studied in detail by Bollobás, Janson and Riordan, which generalises the results we know and love on Erdös-Réyni graphs, and tools from graph theory can be brought to bear on the PDE .

This talk is part of the CMI Student Seminar Series series.

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