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We consider the polynuclear growth (PNG) model in 1+1 dimension with flatinitial condition and no extra constraints. Through theRobinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNGmodel, which consists of a stack of non-intersecting lines, the top one beingthe PNG height. The statistics of the lines is translation invariant and at afixed position the lines define a point process. We prove that for large timesthe edge of this point process, suitably scaled, has a limit. This limit is aPfaffian point process and identical to the one obtained from the edge scalingof Gaussian orthogonal ensemble (GOE) of random matrices. Our results givefurther insight to the universality structure within the KPZ class of 1+1dimensional growth models.Comment: 40 pages, 6 figures, LaTeX; Section 4 is substantially modifie

Polynuclear Growth on a Flat Substrate and Edge Scaling of GOE Eigenvalues