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Published August 2000 | Submitted
Journal Article Open

Limiting Distributions for a Polynuclear Growth Model with External Sources

Abstract

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 Prähofer and Spohn. 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.

Additional Information

© 2000 Plenum Publishing Corporation. Received March 27, 2000. The authors greatly appreciate many enlightening conversations and communications with Michael Prähofer and Herbert Spohn who brought our interest to this problem.

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