7 papers
Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup
Yifan Gao, Ruixuan Li, Xinyi Li
We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection…
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…
Bivariate partial mapping for detecting causality in complex non-autonomous system
Yang Ni, Changqing Liu, Yifan Zhang +4
Identifying causality is fundamental for human understanding of the world, where complex non-autonomous systems such as species population changes, brain activities, etc. are exten…
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…
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…
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…