随机树上及非负整数上的非齐次随机环境中的随机游走
Random walk in a non-homogeneous random environment on some random trees and the non-negative integers
浏览论文内容
中文总结 AI 辅助
本文研究非齐次随机环境中随机树及非负整数上的随机游走，给出类型尖锐阈值并利用平均退出时间与速度关系求出速度，附有极限公式。
中文摘要 AI 辅助
本文考虑了在两类随机树及非负整数上的非齐次随机环境中的随机游走。这里的随机树的后代分布依赖于父代的代数。我们给出了随机树上及非负整数上的随机环境中随机游走类型的尖锐阈值，直至临界情形。然后，我们求出了非负整数上及随机球对称树上的随机游走速度。我们使用了基于顶点平均退出时间与速度之间关系的方法。同时，我们讨论了可由这些结果推导出的几个特殊情况。我们还在附录中包含了序列与级数的许多极限公式，这些公式对本研究及其他研究都有帮助。
英文摘要
In this paper, we consider a random walk in a non-homogeneous random environment on two types of random trees and non-negative integers. The random trees here have progeny distributions that depend on the parent's generation. We provide a sharp threshold for the type of the random walk in a random environment on the random trees and the non-negative integers, up to the critical case. Then, we find the speed of the random walk on the non-negative integers and on random spherically symmetric trees. We use the method based on the relationship between the mean exit time from a vertex and speed. Meanwhile, we discuss several special cases that could be derived from those results. We also include many limiting formulas for sequences and series in the appendix, which are helpful for this study and others.
发表机构
- The University of Texas Rio Grande Valley（德克萨斯大学里奥格兰德河谷分校）
- HUN-REN Wigner RCP Budapest, University Pannonia（匈牙利研究与创新网络温格研究合作中心布达佩斯，潘诺尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
