Limit theorems for random walks on a strip in subdiffusive regimes
Limit theorems for random walks on a strip in subdiffusive regimes
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次扩散区域带上随机游走的极限定理
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
I. Goldsheid
中科院分区：
文献类型：
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作者：
Dmitry Dolgopyat;I. Goldsheid
我们研究了在次扩散区域的淬灭随机环境 (RE) 中瞬态随机游走 (RW) 的占用时间的渐近行为。作为更传统的研究对象的击球时间的渐近行为是完全相同的。作为一个特例，我们解决了一个长期存在的问题，即在一维晶格上描述具有有界跳跃的 RW 的渐近行为。我们的技术源于我们之前关于 RE 中简单 RW 的工作 (Dolgopyat 和 Goldsheid 2012 Commun. Math. Phys. 315 241–77) 以及 Bolthausen 和 Goldsheid (2000 Commun. Math. Phys. 214 429–47; 2008 Commun. Math. Phys. 278) 中使用的思想的发展253–88）和 Goldsheid（2008 Probab. Theory Relat. Fields 141 471–511）研究带上的随机游走。
We study the asymptotic behaviour of occupation times of a transient random walk (RW) in a quenched random environment (RE) on a strip in a subdiffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is exactly the same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a RW with bounded jumps on a one-dimensional lattice. Our technique results from the development of ideas from our previous work (Dolgopyat and Goldsheid 2012 Commun. Math. Phys. 315 241–77) on the simple RWs in RE and those used in Bolthausen and Goldsheid (2000 Commun. Math. Phys. 214 429–47; 2008 Commun. Math. Phys. 278 253–88) and Goldsheid (2008 Probab. Theory Relat. Fields 141 471–511) for the study of random walks on a strip.