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Abstract: We consider critical planar site percolation on the triangular lattice and derive sharp estimates on asymptotics of the probability of half-plane $j$-arm events for $j\geq 1$ and whole-plane (polychromatic) $j$-arm events for $j>1$ under some specific boundary conditions. We also obtain up-to-constant estimates for other boundary conditions in the whole-plane case. These estimates greatly improve previous ones and solve a problem of Schramm (Proc. of ICM, 2006). In the course of proof, we also obtain a super-strong separation lemma, which confirms a conjecture by Garban, Pete and Schramm (J. Amer. Math. Soc., 2013) and is of independent interest. This is joint work in progress with Hang Du (PKU), Yifan Gao (PKU) and Zijie Zhuang (UPenn).
Bio: Dr. Xinyi Li is currently an assistant professor at Peking University. He received his Ph.D. in mathematics from ETH Zurich in 2016 under the supervision of Professor Alain-Sol Sznitman. His research focuses on Probability theory and statistical physics.
