We study an oriented first passage percolation model for the evolution of a river delta. This model is exactly solvable and occurs as the low temperature limit of the beta random walk in random environment. We analyze the asymptotics of an exact formula from [13] to show that, at any fixed positive time, the width of a river delta of length L approaches a constant times L2/3 with Tracy-Widom GUE fluctuations of order L4/9. This result can be rephrased in terms of particle systems. We introduce an exactly solvable particle system on the integer half line and show that after running the system for only finite time the particle positions have Tracy-Widom fluctuations.
CITATION STYLE
Barraquand, G., & Rychnovsky, M. (2019). Tracy-Widom Asymptotics for a River Delta Model. In Springer Proceedings in Mathematics and Statistics (Vol. 282, pp. 483–522). Springer New York LLC. https://doi.org/10.1007/978-3-030-15096-9_17
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