Anomalous impact in reaction-diffusion models
  We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets. 
Iacopo Mastromatteo, Bence Toth and Jean-Philippe Bouchaud
cond-mat.stat-mech q-fin.TR