Condensation of SIP particles and sticky Brownian motion

Mario Ayala, Gioia Carinci, Frank Redig

Published 2019-06-24Version 1

We prove convergence to sticky Brownian motion for the difference of positions of two SIP particles in the condensation regime using Mosco convergence of Dirichlet forms. This extends some of the results of \cite{carinci2017exact}. Our approach also implies the convergence of transition probabilities of the form $p_t(x,0)$ for the difference process. With this convergence, using self-duality we obtain an explicit scaling for the variance of the density field in the condensation regime.