TracyWidom asymptotics for a river delta model
Abstract
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 [4] to show that, at any fixed positive time, the width of a river delta of length $L$ approaches a constant times $L^{2/3}$ with TracyWidom GUE fluctuations of order $L^{4/9}$. 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 TracyWidom fluctuations.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1807.01824
 Bibcode:
 2018arXiv180701824B
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 60B20;
 82B23;
 82C43;
 82C22;
 60F05
 EPrint:
 34 pages, 5 figures