Limiting distributions for a polynuclear growth model with external sources. (English) Zbl 0976.82043

Baik, Jinho; Rains, Eric M.

J. Stat. Phys. 100, No. 3-4, 523-541 (2000).

Summary: The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by M. Prähofer and H. Spohn [Physica A 279, 342-352 (2000; Zbl 0976.82045)]. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.

MSC:

82C41	Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
60K35	Interacting random processes; statistical mechanics type models; percolation theory
82C24	Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics

Keywords:

directed polymer; limiting distribution; polynuclear growth; Tracy-Widom functions; random matrix; discrete totally asymmetric exclusion process