$\mathbb{Z}$上暂态激发随机游走的最长停留时间
概率论
2026-05-27 v2
摘要
我们考虑 上的暂态激发随机游走，研究当前最受访问位点的停留时间的渐近行为。特别地，我们的结果表明，与随机环境中的随机游走相反，暂态激发随机游走并不会在其最常访问（截至当前时刻访问次数最多）的位点上花费渐近意义上正比例的时间。
引用
@article{arxiv.1111.1254,
title = {Maximum occupation time of a transient excited random walk on Z},
author = {Reza Rastegar and Alexander Roitershtein},
journal= {arXiv preprint arXiv:1111.1254},
year = {2026}
}
备注
Revised version. The proof has been updated to clarify the passage from the excited random walk to the associated branching-process representation, using a triangular-array formulation rather than only fixed-level distributional identities. Several related renewal and Borel--Cantelli arguments have also been tightened