Scaling limit of the occupation measure of random walk cut points

Yifan Gao; Xinyi Li; Petr Panov; Daisuke Shiraishi

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arXiv · 2310.09592

Scaling limit of the occupation measure of random walk cut points

Yifan Gao·Xinyi Li·Petr Panov·Daisuke Shiraishi

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Abstract

We consider the occupation measure of the cut points of a simple random walk on a $d$-dimensional cubic lattice for $d = 2, 3$, and we show that the scaling limit of the occupation measure in weak topology is the natural fractal measure on the Brownian cut points defined via its Minkowski content.

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Yifan Gao, Xinyi Li, Petr Panov, Daisuke Shiraishi. 2023-10-14. Scaling limit of the occupation measure of random walk cut points. https://arxiv.org/abs/2310.09592

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