LOCALIZATION OF A 2-DIMENSIONAL RANDOM-WALK WITH AN ATTRACTIVE PATH INTERACTION

• 成果类型: Article
• 署名作者: BOLTHAUSEN, E
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988734
• 发表日期: 1994
• 页码: 875-918
• 关键词: markov process expectations; asymptotic evaluation; large time

摘要

We consider an ordinary, symmetric, continuous-time random walk on the two-dimensional lattice Z2. The distribution of the walk is transformed by a density which discounts exponentially the number of points visited up to time T. This introduces a self-attracting interaction of the paths. We study the asymptotic behavior for T --> infinity. It turns out that the displacement is asymptotically of order T1/4. The main technique for proving the result is a refined analysis of large deviation probabilities. A partial discussion is given also for higher dimensions.