8 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…
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…
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…
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…
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…
A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents
Yifan Gao, Xinyi Li, Yifan Li +2
We show that a domain in with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that t…
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 -dimensiona…
Scaling limit of the occupation measure of random walk cut points
Yifan Gao, Xinyi Li, Petr Panov +1
We consider the occupation measure of the cut points of a simple random walk on a -dimensional cubic lattice for , and we show that the scaling limit of the occupation…