6 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…
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…
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…
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…