Interacting Brownian motions in the Kadar-Parisi-Zhang universality class

A widely studied model from statistical physics consists of many (one-dimensional) Brownian motions interacting through a pair potential. The large scale behavior of this model has has been investigated by Varadhan, Yau, and others in the 90's. As a crucial property the model satisfies time-reversibility (alias detailed balance). Once this symmetry is broken, generically one crosses into the KPZ class. Two specific examples will be discussed.