Slow relaxation, dynamic transitions and extreme value statistics in   disordered systems
  We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase transition in these models to the extreme value statistics of the associated random energy landscape. 
Kristina Van Duijvendijk (MSC), Gr\'egory Schehr (LPT), Fr\'ed\'eric   Van Wijland (MSC)