Local and global behavior of the subcritical contact process

We will describe the scaling limit of the subcritical contact process in terms of a marked Poisson point process and a quasi-stationary distribution, and discuss the question of uniqueness of the QSD in this and other contexts. Based on joint works with E. Andjel, F. Ezanno and P. Groisman, with Aurelia Deshayes, and with F. Arrejoría and P. Groisman.