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math.PR2025
Non-existence of several random fractals in Brownian motion and Brownian loop soup
Yifan Gao, Xinyi Li, Runsheng Liu +1
We develop a unified approach to establish the non-existence of three types of random fractals: (1) the pioneer triple points of the planar Brownian motion, answering an open quest…
math.PR2025
Convergence in natural parametrization of random walk frontier
Yifan Gao, Xinyi Li, Runsheng Liu +2
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…