Planar Brownian motion and Gaussian multiplicative chaos
Planar Brownian motion and Gaussian multiplicative chaos
复制标题
平面布朗运动和高斯乘性混沌
作者：
A. Jego
通过对小圆局部时的平方根取幂，构造了平面布朗运动局部时的高斯乘性混沌测度的模拟。我们还考虑了一个平坦的措施支持的点，其本地时间是在一个恒定的所需的厚度水平，并显示两个对象之间的简单关系。我们的结果扩展了Bass、Burdzy和Khoshnevisan的结果，特别是涵盖了整个L^1 $相或亚临界区。这些结果使我们能够获得一个非退化的限制适当重新缩放大小的厚点，从而大大细化估计Dembo，佩雷斯，罗森和Zeitouni。
We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Brownian motion by exponentiating the square root of the local times of small circles. We also consider a flat measure supported on points whose local time is within a constant the desired thickness level and show a simple relation between the two objects. Our results extend those of Bass, Burdzy and Khoshnevisan and in particular cover the entire $L^1$-phase or subcritical regime. These results allow us to obtain a nondegenerate limit for the appropriately rescaled size of thick points, thereby considerably refining estimates of Dembo, Peres, Rosen and Zeitouni.
影响因子：
0.5
作者：
Berestycki, Nathanael
通讯作者：
Berestycki, Nathanael