Probability and Stochastic Analysis Seminar

Next session

Condensation of SIP particles and sticky Brownian motions

The symmetric inclusion process (SIP) is a particle system with attractive interaction. We study its behavior in the condensation regime attained for large values of the attraction intensity. Using Mosco convergence of Dirichlet forms, we prove convergence to sticky Brownian motion for the distance of two SIP particles. We use this result to obtain, via duality, an explicit scaling for the variance of the density field in this regime, for the SIP initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing particle systems on the infinite lattice. Joint work with M. Ayala and F. Redig.

Note that we are now a joint probability seminar with IMPA. See here: https://sbp.impa.br