The subleading order of two dimensional cover times

被引：30
作者：
Belius, David [1 ]
Kistler, Nicola [2 ]
机构：
[1] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA
[2] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 167卷 / 1-2期
基金：
瑞士国家科学基金会;
关键词：
BROWNIAN-MOTION; 2; DIMENSIONS; RANDOM-WALKS; ASYMPTOTICS; TREES;
D O I：
10.1007/s00440-015-0689-6
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.
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页码：461 / 552
页数：92
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