Anomalous price impact and the critical nature of liquidity in financial   markets
  We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients. 
Bence Toth, Yves Lemperiere, Cyril Deremble, Joachim de Lataillade,   Julien Kockelkoren, Jean-Philippe Bouchaud
q-fin.TR cond-mat.stat-mech physics.soc-ph