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We consider the multi-point equal time height fluctuations of aone-dimensional polynuclear growth model in a half space. For special values ofthe nucleation rate at the origin, the multi-layer version of the model isreduced to a determinantal process, for which the asymptotics can be analyzed.In the scaling limit, the fluctuations near the origin are shown to beequivalent to those of the largest eigenvalue of the orthogonal/symplectic tounitary transition ensemble at soft edge in random matrix theory.Comment: 51 pages, 8 figure

Fluctuations of the One-Dimensional Polynuclear Growth Model in Half-Space