|Location:||MSRI: Simons Auditorium, Online/Virtual|
Exactly Solvable Coagulation Processes, Random Graphs And Large Deviations
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In this talk we present a model where particles interact via a coagulation mechanism and we focus our attention on some particular coagulation kernels that allows to write explicitly the probability to observe any given configuration. We draw connection with random graphs, in particular with the sparse Erd ̋os– R ́enyi random graph and its inhomogeneous generalization. Via this connection it is possible to derive a large deviation principle for the empirical measure of particle sizes at a fix time and to deduce the existence or not of a phase transition, which in this type of models depends on time and it is called gelation. This is an ongoing joint work with Wolfgang König (WIAS and TU Berlin), Tejas Iyer, Heide Langhammer, Elena Magnanini , Robert Patterson (WIAS Berlin).No Notes/Supplements Uploaded