Condensation of SIP Particles and Sticky Brownian Motion

Mario Ayala , Gioia Carinci, Frank Redig

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We study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

Original languageEnglish
Article number40
Number of pages42
JournalJournal of Statistical Physics
Issue number3
Publication statusPublished - 2021


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