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cond-mat.stat-mech2024
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…
math.PR2024
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…
math.PR2024
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…