Localization and fluctuations in non-equilibrium multicomponent coagulating systems

par Marina Ferreira (IMT)

mardi 20 oct. 2026, 09:50 → 10:50 Europe/Paris

We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property: they asymptotically localize into a direction determined by the source or by a flux constraint. As a consequence, the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. Moreover, under an extra symmetry assumption on the coagulation kernel, the fluctuations around the localization direction of the quotient of the multicomponent solution and the one-component solution converge to a multivariate Gaussian probability density function, which is independent of the coagulation kernel. 

This talk is part of a Seminar series on Coagulation and fragmentation dynamics (https://indico.math.cnrs.fr/event/16068/), which is itself part of the CIMI Semester Interacting particles, PDEs and applications (https://indico.math.cnrs.fr/category/816/). It can however be understood without attending the rest of the series.