The two regimes of moderate deviations for the range of a transient walk
The two regimes of moderate deviations for the range of a transient walk
复制标题
瞬态行走范围的两种中等偏差状态
DOI：
--
复制
发表时间：
2021
影响因子：
2
通讯作者：
Bruno Schapira
中科院分区：
文献类型：
--
作者：
A. Asselah;Bruno Schapira
我们获得了五维及更大维度随机游走范围的体积向下适度偏差的尖锐上界和下界。我们的研究结果包括两个制度：高斯制度的小偏差，和拉伸指数制度较大的偏差。在后一种制度，我们表明，条件的中度偏差事件，步行折叠一小部分，其范围内的一个球样的子集。此外，我们提供了新的路径属性，在三维。除了牛顿能力在本研究中发挥的关键作用外，我们还介绍了两个具有普遍意义的原创思想，它们加强了Asselah和Schapira（Sci Éc Norm Supér 50（4）：755-786，2017）中开发的方法。
We obtain sharp upper and lower bounds for the downward moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched exponential regime for larger deviations. In the latter regime, we show that conditioned on the moderate deviations event, the walk folds a small part of its range in a ball-like subset. Also, we provide new path properties, in dimension three as well. Besides the key role Newtonian capacity plays in this study, we introduce two original ideas, of general interest, which strengthen the approach developed in Asselah and Schapira (Sci Éc Norm Supér 50(4):755–786, 2017).