Condensation in the inclusion process and related models

We study condensation in the recently introduced inclusion process. For an asymmetric one-dimensional version with closed boundary conditions we show that all but a finite number of particles condense on a single site. This is extended to a general result for independent random variables with different tails, where condensation occurs for the index (site) with the heaviest tail, generalizing also previous results for zero-range processes. For inclusion processes with homogeneous stationary states, we establish condensation in the limit of vanishing diffusion strength in the dynamics, and give several details about how the limit is approached for finite and infinite systems. This is joint work with Frank Redig and Kiamars Vafayi.