Anomalous Impact in Reaction-Diffusion Financial Models

We generalize the reaction-diffusion model A + B -> empty set 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 the 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.