论文标题
重新启动的记录年龄的通用框架
Universal framework for record ages under restart
论文作者
论文摘要
我们提出了一个通用框架，以计算经过随机重新启动的随机时间序列的创纪录年龄统计数据。所提出的框架对基础过程的假设最少，并且还适合治疗超出马尔可夫环境的通用重新启动协议。在基准在$ 1 $ d晶格上进行经典随机步行的框架之后，我们得出了一个普遍的标准，其基础是重新启动对具有最近邻居过渡的通用时间序列的$ n $ th记录的影响。至关重要的是，与简单的第一学期完成相比，该标准包含订单$ n $的罚款，这对重新启动创建记录构成了强大的限制。我们的方法的适用性进一步证明了聚集的过程，在该过程中，我们计算了总体大小的典型增长速率。这个统一的框架为探索在广泛的复杂系统中重新启动的时间序列的记录统计数据铺平了道路。
We propose a universal framework to compute record age statistics of a stochastic time-series that undergoes random restarts. The proposed framework makes minimal assumptions on the underlying process and is furthermore suited to treat generic restart protocols going beyond the Markovian setting. After benchmarking the framework for classical random walks on the $1$D lattice, we derive a universal criterion underpinning the impact of restart on the age of the $n$th record for generic time-series with nearest-neighbor transitions. Crucially, the criterion contains a penalty of order $n$, that puts strong constraints on restart expediting the creation of records, as compared to the simple first-passage completion. The applicability of our approach is further demonstrated on an aggregation-shattering process where we compute the typical growth rates of aggregate sizes. This unified framework paves the way to explore record statistics of time-series under restart in a wide range of complex systems.
