Tracy-Widom asymptotics for a river delta model

@article{Barraquand2017TracyWidomAF,
  title={Tracy-Widom asymptotics for a river delta model},
  author={Guillaume Barraquand and M. Rychnovsky},
  journal={arXiv: Probability},
  year={2017}
}
  • 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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 62 REFERENCES
    Dynamic scaling of growing interfaces.
    • 3,165
    • PDF
    Shape Fluctuations and Random Matrices
    • 1,118
    • Highly Influential
    • PDF
    The Kardar-Parisi-Zhang Equation and Universality Class
    • THE KARDAR-PARISI-ZHANG
    • 2011
    • 333
    • PDF
    Large time asymptotics of growth models on space-like paths I: PushASEP
    • 129
    • PDF
    The Kardar-Parisi-Zhang equation and universality class
    • 199
    • PDF
    Integral Formulas for the Asymmetric Simple Exclusion Process
    • 169
    • PDF
    Asymptotics in ASEP with Step Initial Condition
    • 205
    • PDF
    Universal distributions for growth processes in 1+1 dimensions and random matrices
    • 343
    • PDF
    Macdonald processes
    • 181
    • PDF
    On the distribution of the length of the longest increasing subsequence of random permutations
    • 995
    • PDF