Abstract
Departamento de Fi´sica, Universidad Nacional de San Luis, Chacabuco 917, 5700 San Luis, Argentina~Received 9 January 1997!The three approaches usually used to study surface growth are ~i! master equation, ~ii! stochastic Langevinequation, and ~iii! microscopic models. All of them give the same scaling exponents. Recently, Vvedenskyet al. @Phys. Rev. E 48, 852 ~1993!# derived a stochastic Langevin equation from a master equation of the birthand death type, for the epitaxial growth, demonstrating the equivalence of both approaches. In this paper astochastic Langevin equation is derived from a discrete model. The results are the same as those obtained byVvedensky et al. demonstrating that the three approaches are equivalent. As a nontrivial example, our proce-dure is used to derive the Kardar-Parisi-Zhang~KPZ! equation from the ballistic deposition process. Thismodel with vacancies and overhangs is very difficult to handle, due to the algebraic complications that arisewhen the master equation approach is used. @S1063-651X~97!11905-5#PACS number~s!: 05.40.1jI. INTRODUCTION
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