Discrete polynuclear growth and determinantal processes

Abstract

We consider a discrete polynuclear growth (PNG) process and prove a functioal limit theorem for its convergrence to the Airy process. This generalizes previous results by Pr"ahofer and Spohn. The result enables us to express the GOE largest eigenvalue (Tracy-Widom) distribution in terms of the Airy process. We also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem.

In the new version some parts have been replaced, new material has beeb added and errors corrected

References in corpus (4)

• Local statistics of lattice dimers
• Scale Invariance of the PNG Droplet and the Airy Process
• On Convergence of Moments for Random Young Tableaux and a Random Growth Model
• Optimal tail estimates for directed last passage site percolation with geometric random variables

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