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<p>We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in the context of i.i.d. exponential weights for both zero and near-stationary boundary conditions. A main technical novelty in our approach is a new proof of the left-tail fluctuation upper bound with exponent 3/2 for the last-passage times.</p>

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Coupling Derivation of Optimal-Order Central Moment Bounds in Exponential Last-Passage Percolation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月30日

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  • Elnur Emrah,
  • Nicos Georgiou,
  • Janosch Ortmann

摘要

We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in the context of i.i.d. exponential weights for both zero and near-stationary boundary conditions. A main technical novelty in our approach is a new proof of the left-tail fluctuation upper bound with exponent 3/2 for the last-passage times.