KPZ equation: Galilean-invariance violation, consistency, and fluctuation-dissipation issues in real-space discretization

6 páginas, 1 figura.-- El pdf del artículo es la versión pre-print.Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion equation (with multiplicative noise) through a Hopf-Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We emphasize the importance of the Lyapunov functional as natural starting point for real-space discretization and, in the light of these findings, challenge the mainstream opinion on the relevance of Galilean invariance.HSW and JAR acknowledge financial support from MEC, Spain, through Project CGL2007-64387/CLI. RRD acknowledges financial support from CONICET and UNMdP of Argentina. CE acknowledges financial support from the MICINN, Spain, through Project No. MTM2008-03754. The international collaboration has been facilitated by AECID, Spain, through Projects A/013666/07 and A/018685/08.Peer reviewe