5 papers
Percolation of discrete GFF in dimension two II. Connectivity properties of two-sided level sets
Yifan Gao, Pierre Nolin, Wei Qian
We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in 2D. For a DGFF defined in a box with side length , for large enough, t…
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…
Arm events in critical planar loop soups
Yijie Bi, Yifan Gao, Pierre Nolin +1
We establish up-to-constants estimates for arm events in the Brownian loop soup on the 2D metric graph associated with the square lattice. More specifically, we consider two natura…
Up-to-constants estimates on four-arm events for simple conformal loop ensemble
Yifan Gao, Pierre Nolin, Wei Qian
We prove up-to-constants estimates for a general class of four-arm events in simple conformal loop ensembles, i.e. CLE for . The four-arm events that we conside…
Backbone exponent and annulus crossing probability for planar percolation
Pierre Nolin, Wei Qian, Xin Sun +1
We report the recent derivation of the backbone exponent for 2D percolation. In contrast to previously known exactly solved percolation exponents, the backbone exponent is a transc…