当测地线在有向景观中变为刚性时

Pub Date : 2021-06-13 DOI:10.1214/22-ecp484

Zhipeng Liu

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引用次数: 3

摘要

当一点（p；q）的有向景观的值L足够大时，从p到q的测地线是刚性的，其位置围绕其预期为L−1/4阶。我们进一步证明，在测地线的中点，测地线的位置和适当缩放后的定向景观的值收敛到两个独立的高斯。

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When the geodesic becomes rigid in the directed landscape

When the value L of the directed landscape at a point ( p ; q ) is suﬃciently large, the geodesic from p to q is rigid and its location ﬂuctuates of order L − 1 / 4 around its expectation. We further show that at a midpoint of the geodesic, the location of the geodesic and the value of the directed landscape after appropriate scaling converge to two independent Gaussians.

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