论文标题
指导景观中的三半变化
Three-halves variation of geodesics in the directed landscape
论文作者
论文摘要
我们表明，有指示景观中的大地测量学具有$ 3/2 $变化，而沿大地测量学的重量功能具有立方变化。 我们表明，围绕内部点的大地测量及其景观环境具有小规模的限制。该极限是根据布朗贝塞尔边界条件的定向景观给出的。不同内部点周围的环境在渐近独立。 我们给出带有最佳指数的尾部边界，用于测量和重量功能增量。 作为我们结果的应用，我们表明地球学不是Hölder-$ 2/3 $，而权重功能不是Hölder-$ 1/3 $，尽管已知这些对象是Hölder，其中所有较低的指数。
We show that geodesics in the directed landscape have $3/2$-variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscape environment around an interior point has a small-scale limit. This limit is given in terms of the directed landscape with Brownian-Bessel boundary conditions. The environments around different interior points are asymptotically independent. We give tail bounds with optimal exponents for geodesic and weight function increments. As an application of our results, we show that geodesics are not Hölder-$2/3$ and that weight functions are not Hölder-$1/3$, although these objects are known to be Hölder with all lower exponents.
