AI 中文总结
研究N个通过共享轨迹场相互作用的一维随机漫步者，推导对轨迹有饱和响应的自相互作用漫步者的持续指数和分裂概率精确表达式，发现漫步者探索方式不影响分裂概率，为相关系统首次通过现象建立框架。
AI 中文摘要
环境中编码的记忆介导了活性主体之间的相互作用，从追踪轨迹的生物体到沉积持久轨迹的合成活性物质。虽然已知这种记忆会强烈影响传输，但其对集体首次通过现象的影响在很大程度上仍未得到探索。在此，我们研究通过共享轨迹场相互作用的N个一维随机漫步者。我们表征了在固定目标处第k（在N个中）个到达时间，以及在[0,1]中恰好k个漫步者在到达一个边界之前到达另一个边界的概率。对于对轨迹具有饱和响应的广泛的自相互作用漫步者类别，我们推导出了相应的持续指数和分裂概率的精确表达式。令人惊讶的是，尽管共同环境产生了强烈的历史依赖相关性，但无论漫步者是同时探索还是一个接一个地探索，分裂概率完全相同。对于非饱和轨迹相互作用，这种不变性会失效。我们的结果来自集体轨迹场的精确表示，并为通过持久环境记忆耦合的系统中的首次通过现象建立了一个框架。
英文摘要
Memory encoded in the environment mediates interactions between active agents, from trail-following organisms to synthetic active matter depositing persistent tracks. Although such memory is known to strongly affect transport, its consequences for collective first-passage phenomena remain largely unexplored. Here we study $N$ one-dimensional random walkers interacting through a shared trail field. We characterize the $k^{\rm th}$ (among $N$) arrival time at a fixed target, and the probability that exactly $k$ walkers in $[0,1]$ reach one boundary before the other. For the broad class of self-interacting walkers with a saturating response to the trail, we derive exact expressions for the corresponding persistence exponents and splitting probabilities. Strikingly, despite the strong history-dependent correlations generated by the common environment, splitting probabilities are exactly identical whether walkers explore simultaneously or one after another. This invariance breaks down for nonsaturating trail interactions. Our results follow from an exact representation of the collective trail field and establish a framework for first-passage phenomena in systems coupled through persistent environmental memory.
CommentsArticle: 6 pages; Supplementary: 28 pages
