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• W3088097989 abstract "Abstract We provide the first nontrivial upper bound for the chemical distance exponent in two‐dimensional critical percolation. Specifically, we prove that the expected length of the shortest horizontal crossing path of a box of side length n in critical percolation on ℤ 2 is bounded by Cn 2 − δ π 3 ( n ) for some δ > 0 , where π 3 ( n ) is the “three‐arm probability to distance n .” This implies that the ratio of this length to the length of the lowest crossing is bounded by an inverse power of n with high probability. In the case of site percolation on the triangular lattice, we obtain a strict upper bound for the exponent of 4/3 . The proof builds on the strategy developed in our previous paper, but with a new iterative scheme, and a new large deviation inequality for events in annuli conditional on arm events, which may be of independent interest. © 2020 Wiley Periodicals LLC" @default.
• W3088097989 created "2020-10-01" @default.
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• W3088097989 date "2020-09-23" @default.
• W3088097989 modified "2023-10-18" @default.
• W3088097989 title "Strict Inequality for the Chemical Distance Exponent in<scp>Two‐Dimensional</scp>Critical Percolation" @default.
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• W3088097989 doi "https://doi.org/10.1002/cpa.21945" @default.
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