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Discrete polynuclear growth and determinantal processes. (English) Zbl 1031.60084

The paper generalizes previous results by M. Prähofer and H. Spohn [J. Stat. Phys. 108, 1071-1106 (2002; Zbl 1025.82010)] on the polynuclear growth process. A functional limit theorem for the convergence of this process to the Airy process is proved. The result enables one to express the Widom-Tracy random-matrix level distribution [C. A. Tracy and H. Widom, Commun. Math. Phys. 159, 151-174 (1994; Zbl 0789.35152)] in terms of the Airy process. Following the author’s own work on shape fluctuations and random matrices [ibid. 209, 437-476 (2000; Zbl 0969.15008)], new results and conjectures are given about transversal fluctuations in the percolation problem. The general class of measures given by products of determinants is described, together with their determinantal correlation functions.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
60F17 Functional limit theorems; invariance principles
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