Tracy-Widom asymptotics for a river delta model

  title={Tracy-Widom asymptotics for a river delta model},
  author={Guillaume Barraquand and M. Rychnovsky},
  journal={arXiv: Probability},
  • Guillaume Barraquand, M. Rychnovsky
  • Published 2017
  • Mathematics, Physics
  • arXiv: Probability
  • 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 Tracy-Widom GUE fluctuations of order $L^{4/9}$. This result can be rephrased in terms of particle systems. We… CONTINUE READING

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