Limiting Distributions for a Polynuclear Growth Model with External Sources |
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Authors: | Jinho Baik Eric M. Rains |
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Affiliation: | (1) Department of Mathematics, Princeton University, Princeton, New Jersey, 08544;(2) Institute for Advanced Study, Princeton, New Jersey, 08540;(3) AT&T Research, New Jersey, Florham Park, New Jersey, 07932 |
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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. |
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Keywords: | PNG ASEP directed polymer random matrix limiting distribution |
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