Invited review: KPZ. Recent developments via a variational formulation


  • Horacio S. Wio Instituto de Fisica de Cantabria Universidad de Cantabria
  • Roberto R. Deza
  • Carlos Escudero
  • Jorge A. Revelli



Theory and models of film growth, renormalization group methods, stochastic analysis methods


Recently, a variational approach has been introduced for the paradigmatic Kardar-Parisi-Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits. Such expansion becomes naturally truncated at third order, giving rise to a nonlinear stochastic partial differential equation to be regarded as a gradient-flow counterpart to the KPZ equation. A dynamic renormalization group analysis at one-loop order of this new mesoscopic model yields the KPZ scaling relation $\alpha + z = 2$, as a consequence of the exact cancelation of the different contributions to vertex renormalization. This result is quite remarkable, considering the lower degree of symmetry of this equation, which is in particular not Galilean invariant. In addition, this scheme is exploited to inquire about the dynamical behavior of the KPZ equation through a path-integral approach. Each of these aspects offers novel points of view and sheds light on particular aspects of the dynamics of the KPZ equation.


Received: 25 June 2013, Accepted: 10 December 2013; Reviewed by: F. Reis, Instituto de Fisica, Univ. Fed. Fluminense, Brazil; Edited by: R. Dickman; DOI:

Cite as: H S Wio, R R Deza, C Escudero, J A Revelli, Papers in Physics 5, 050010 (2013)


Author Biography

Horacio S. Wio, Instituto de Fisica de Cantabria Universidad de Cantabria

Full Professor of Theoretical Physics

Daprtamento de Fisica Moderna, Facultad de Ciencias, Universidad de Cantabria

Open Review



How to Cite

Wio, H. S., Deza, R. R., Escudero, C., & Revelli, J. A. (2014). Invited review: KPZ. Recent developments via a variational formulation. Papers in Physics, 5, 050010.