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Sharp asymptotics for arm probabilities in critical planar percolation
Hang Du, Yifan Gao, Xinyi Li +1
In this work, we consider critical planar site percolation on the triangular lattice and derive sharp estimates on the asymptotics of the probability of half-plane -arm events f…
On large deviations and intersection of random interlacements
Xinyi Li, Zijie Zhuang
We investigate random interlacements on with , and derive the large deviation rate for the probability that the capacity of the interlacement set in a macr…
On Natural Measures of SLE- and CLE-Related Random Fractals
Gefei Cai, Xinyi Li
In this paper, we construct and then prove the up-to constants uniqueness of the natural measure on several random fractals, namely the SLE cut points, SLE boundary touching points…
One-point function estimates for loop-erased random walk in three dimensions
Xinyi Li, Daisuke Shiraishi
In this work, we consider loop-erased random walk (LERW) in three dimensions and give an asymptotic estimate on the one-point function for LERW and the non-intersection probability…
Shape theorem and surface fluctuation for Poisson cylinders
Marcelo Hilario, Xinyi Li, Petr Panov
In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any , conditioned on the origin b…
Natural parametrization of percolation interface and pivotal points
Nina Holden, Xinyi Li, Xin Sun
We prove that the interface of critical site percolation on the triangular lattice converges to SLE in its natural parametrization, where the discrete interface is parametrized…