The talk will deal with processes of gaps between competing particles on the real line and half-line. Such evolutions were studied first by Ruzmaikina and Aizenman (2005) in the context of the Sherrington-Kirkpatrick model of spin glasses and later by Chatterjee and Pal (2007) and Pal and Pitman (2008) in the context of models for the capital distribution in a financial market. I will give...