Discrete polynuclear growth and determinantal processes

We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prahofer and Spohn. The result enables us to express the F-1 GOE 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. Furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions.