6 papers
Loop pruning and downward deviations for maximum local time of discrete-time simple random walks
Xinyi Li, Yushu Zheng
We study downward deviations of the maximum local time of the discrete-time simple random walk on , . In our previous paper \cite{li2026ldmaxlocal}, the corre…
Wireless large AI model: shaping the AI-empowered future of 6G and beyond
Fenghao Zhu, Xinquan Wang, Siming Jiang +22
The emergence of sixth-generation and beyond communication systems is expected to fundamentally transform digital experiences through introducing unparalleled levels of intelligenc…
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…
One-arm probabilities for the two-dimensional metric-graph and discrete Gaussian free field
Yijie Bi, Yifan Gao, Xinyi Li
We study the one-arm probability in the level-set percolation of the discrete and metric-graph Gaussian free field (GFF) defined on a box with Dirichlet boundary conditions. For th…
Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
Sarai Hernandez-Torres, Xinyi Li, Daisuke Shiraishi
In this work, we consider the scaling limit of loop-erased random walk (LERW) in three dimensions and prove that the limiting occupation measure is equivalent to its -dimension…
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…