In order to study the depinning transition in presence of strong disorder, Derrida and Retaux (J. Stat. Phys. (2014)) introduced a discrete-time max-type recursive model. It is believed that for a large class of recursive models, including the Derrida and Retaux model, there are highly non-trivial universalities on the critical behavior of the free energy. In this talk, we will review some recent results and open questions on the Derrida and Retaux model as well as on its continuous-time version. The talk is based on joint works with Xinxing Chen, Victor Dagard, Bernard Derrida, Mikhail Lifshits, Bastien Mallein, Michel Pain and Zhan Shi.
