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arxiv: 2504.13743 · v1 · pith:4R4QFNZZ · submitted 2025-04-18 · math.PR

Convergence in natural parametrization of random walk frontier

Yifan Gao , Xinyi Li , Runsheng Liu , Xiangyi Liu , Daisuke Shiraishi This is my paper

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

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