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<p>In this paper, we show that the frontier of the planar random walk converges weakly under the natural parametrization to that of planar Brownian motion. As an intermediate result, we also show the convergence of the renormalized occupation measure.</p>

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Convergence in natural parametrization of random walk frontier

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Yifan Gao,
  • Xinyi Li,
  • Runsheng Liu,
  • Xiangyi Liu,
  • Daisuke Shiraishi

摘要

In this paper, we show that the frontier of the planar random walk converges weakly under the natural parametrization to that of planar Brownian motion. As an intermediate result, we also show the convergence of the renormalized occupation measure.