Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues

Details Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues

2004-02-19

arxiv.org/abs/math-ph/0402053v3

Comm. Math. Phys., 252 (2004), 77-109

Physics

Mathematical Physics

40 pages, 6 figures, LaTeX; Section 4 is substantially modified

Scientific paper

10.1007/s00220-004-1204-6

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. Through the Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG model, which consists of a stack of non-intersecting lines, the top one being the PNG height. The statistics of the lines is translation invariant and at a fixed position the lines define a point process. We prove that for large times the edge of this point process, suitably scaled, has a limit. This limit is a Pfaffian point process and identical to the one obtained from the edge scaling of Gaussian orthogonal ensemble (GOE) of random matrices. Our results give further insight to the universality structure within the KPZ class of 1+1 dimensional growth models.

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