title: Generalized discretization of the Kardar-Parisi-Zhang equation.
abstract: We report the generalized spatial discretization of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. We solve exactly the steady state probability density function for the discrete heights of the interface, for any discretization scheme. We show that the discretization prescription is a consequence of each particular model. We derive the discretization prescription of the KPZ equation for the ballistic deposition model.
authors.affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata Funes 3350, B7602AYL Mar del Plata, Argentina.
authors.forename: R C
authors.initials: RC
authors.lastname: Buceta