The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems has led to a large literature on the modelling of temporally correlated movement paths. Despite the substantial body of work, little progress has been made to determine the dynamical properties of various transport related quantities, including the first-passage or first-hitting probability to one or multiple absorbing targets when space is bounded. To bridge this knowledge gap we generalise the renewal theory of first-passage and splitting probabilities to correlated discrete variables. We do so in arbitrary dimensions on a lattice for the so-called correlated or persistent random walk, the one step non-Markovian extension of the simple lattice random walk in bounded and unbounded space. We focus on bounded domains and consider both persistent and anti-persistent motion in hypercubic lattices as well as the hexagonal lattice. The discrete formalism allows us to extend the notion of the first-passage to that of the directional first-passage, whereby the walker must reach the target from a prescribed direction for a hitting event to occur. As an application to spatio-temporal observations of correlated moving cells that may be either repelled or attracted to hard surfaces, we compare the first-passage statistics to a target within a reflecting domain depending on whether an interaction with the reflective interface invokes a reversal of the movement direction or not. With strong persistence we observe multi-modality in the first-passage distribution in the former case, which instead is greatly suppressed in the latter.
Exact collective first-passage statistics of N trail-interacting walkers
Laboratoire Jean Perrin, CNRS/Sorbonne Université（让·佩兰实验室，法国国家科学研究中心/索邦大学）；Collège de France（法兰西公学院）；Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université（凝聚态物质理论物理实验室，法国国家科学研究中心/索邦大学）
Diffusion in a wedge geometry: First-Passage Statistics under Stochastic Resetting
Cochin university of science and technology（科钦科技大学）；The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India（泰米尔纳德邦金奈塔拉马尼 CIT 校园数学科学研究所）；Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India（印度孟买安努沙克提纳加尔霍米·巴哈国家学院培训楼）
Active Brownian Dynamics in Channels: First-Passage and Spatiotemporal Properties via Siegmund Duality
Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence, Physics of Life, TU Dresden（德累斯顿工业大学生命物理卓越集群）
Mean first passage times of higher-dimensional velocity jump processes
California State University at Northridge（北岭加州州立大学）；University of California at Los Angeles（加利福尼亚大学洛杉矶分校）；University of Notre Dame（圣母大学）；University of Alberta（阿尔伯塔大学）
Persistent search in confined domains: a velocity-jump process model
我们分析了有界区域上持续搜索单个目标的速度跳跃过程模型。弹道导弹沿着弹道轨迹前进，并在与目标边界碰撞时被吸收。当到达域边界时，微处理器为其新轨迹选择随机方向。对于圆形域和目标，我们可以使用搜索过程的马尔可夫链近似来近似平均首次通过时间（MFPT）。我们的分析和数值模拟表明，找到目标的时间减少目标更接近域边界。当区域内方向切换概率较小时，发现目标的时间随转向概率的增加而略有减少。我们还扩展了我们的退出时间分析的情况下，分区域，其中有一个单一的目标在多个不相交的子域之一。给定域之间的平均过渡时间$\langle T \rangle$，我们发现，最小化找到目标的时间的最佳过渡率服从$β_{\rm min} \propto 1/ \sqrt{\langle T \rangle}$。
Tethering effects on first-passage variables of lattice random walks in linear and quadratic focal point potentials
SISSA – International School for Advanced Studies（国际高等研究院）；Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche（复杂系统研究所，意大利国家研究委员会）；School of Engineering Mathematics and Technology, University of Bristol（布里斯托大学工程数学与技术学院）
Mirror transitions in diffusion with stochastic resetting confined on a ring
Universidad Autónoma Metropolitana（墨西哥自治 metropolitan 大学）；Universidad Autónoma de Chiapas（恰帕斯自治大学）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）
