发表机构
Institute of Research and Development, Duy Tan University; Duy Tan University; Faculty of Natural Sciences, Duy Tan University（发展研究院; 大雁大学; 自然科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究双记忆通道象随机游走，证明p=11/16为精确递归-暂态阈值，并确定暂态区间的逃逸速率及p=7/8时的逃逸尺度。
AI 中文摘要
我们研究了由Saha [Phys. Rev. E 106, L062105 (2022)]引入的具有双记忆通道的一维象随机游走，其记忆参数为p∈(0,1)。Maulik、Roy和Sadhukhan [arXiv:2509.10225]证明了当p≤11/16时游走是递归的，当p>7/8时是暂态的，但留下了11/16<p≤7/8这一区间未解决。我们通过证明p=11/16是精确的递归-暂态阈值，并确定游走在整个暂态区域内从原点逃逸的速度，填补了这一空白。对于11/16<p<7/8，我们还证明了由Maulik、Roy和Sadhukhan获得的标度极限几乎必然非零。在p=7/8时，我们证明了游走是暂态的，具有零渐近速度，并以n/√(log n)的尺度逃逸。
英文摘要
We study the one-dimensional elephant random walk with two memory channels introduced by Saha [Phys.\ Rev.\ E \textbf{106}, L062105 (2022)] with memory parameter $p\in(0,1)$. Maulik, Roy and Sadhukhan [arXiv:2509.10225] proved recurrence for $p\le11/16$ and transience for $p>7/8$, leaving the range $11/16<p\le7/8$ open. We close this gap by proving that $p=11/16$ is the exact recurrence--transience threshold and by determining how fast the walk escapes from the origin throughout the transient regime. For $11/16<p<7/8$, we also show that the scaling limit obtained by Maulik, Roy and Sadhukhan is almost surely nonzero. At $p=7/8$, we prove that the walk is transient with zero asymptotic velocity and escapes at the scale $n/\sqrt{\log n}$.
