6 citations · 6 across the 6 of their papers we have counts for
6 papers
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 consider…
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…
Percolation of discrete GFF in dimension two I. Arm events in the random walk loop soup
Yifan Gao, Pierre Nolin, Wei Qian
In this work, which is the first part of a series of two papers, we study the random walk loop soup in dimension two. More specifically, we estimate the probability that two large…
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, th…
Backbone exponent for two-dimensional percolation
Pierre Nolin, Wei Qian, Xin Sun +1
We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. C…