By Leonardo Rolla, Universidad de Buenos Aires

Modern statistical mechanics offers a large class of driven-dissipative stochastic systems that naturally evolve to a critical state, of which activated random walks is perhaps the best example. The main pursuit in this field is to describe the critical behavior, the scaling relations and critical exponents of such systems, and whether the critical density in the infinite system is the same as the equilibrium density in their driven-dissipative finite-volume version. These questions are however far beyond the reach of existing techniques. In this talk we will report on the progress obtained in recent years, and discuss some of the open problems.