论文标题
在具有相关过渡的网络多粒子系统中重置随机重置
Stochastic resetting in a networked multiparticle system with correlated transitions
论文作者
论文摘要
许多物理，生物学和社会技术系统的状态通过将平稳的局部过渡和突然重置事件结合到一组参考值来发展。重置机制的包含不仅提供了建模各种现实系统的可能性，而且还导致有趣的新现象学在无复位病例中不存在。但是，研究了随机重置的大多数模型都解决了有限数量的无关变量的情况，通常是一个单个变量，例如非相互作用的随机步行者的位置。在这里，我们通过将网络增长的过程（以节点删除为随机重置问题）构建来克服这一限制，在这种问题中，任意大量的自由度耦合并相互影响，无论是在重置和非排序（增长）事件中。我们发现该模型的确切，全职解决方案，并且几种平衡的特性的特征是生长和重置速率的函数，例如时间依赖性的渗透样相变的出现以及第一学期统计。对重置进行重置的耦合多粒子系统是随机重置理论的必要概括，此处介绍的模型是这种概括的说明性，自然和可解决的示例。
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the possibility of modeling a wide variety of realistic systems but also leads to interesting novel phenomenology not present in reset-free cases. However, most models where stochastic resetting is studied address the case of a finite number of uncorrelated variables, commonly a single one, such as the position of non-interacting random walkers. Here we overcome this limitation by framing the process of network growth with node deletion as a stochastic resetting problem where an arbitrarily large number of degrees of freedom are coupled and influence each other, both in the resetting and non-resetting (growth) events. We find the exact, full-time solution of the model, and several out-of-equilibrium properties are characterized as function of the growth and resetting rates, such as the emergence of a time-dependent percolation-like phase transition, and first-passage statistics. Coupled multiparticle systems subjected to resetting are a necessary generalization in the theory of stochastic resetting, and the model presented herein serves as an illustrative, natural and solvable example of such a generalization.
