漂移马尔可夫链中的极端事件统计
Extreme Event Statistics in a Drifting Markov Chain
摘要：
我们分析极端事件统计实验实现马尔可夫链的各种漂移。我们的马尔可夫链是单个原子在一维周期势中扩散的单个轨道。基于超过500个单独的原子痕迹，我们验证了适用性的Sparre Andersen定理，我们的系统，尽管存在漂移。我们提出了详细的分析，我们的系统的四个不同的罕见事件的统计：分布的极端值，记录值，极端值发生在链中，并在链中的记录的数量。我们观察到，对于我们的数据，极端事件分布的形状主要由从原子轨迹中提取的潜在指数距离分布决定。此外，我们发现，即使是很小的漂移影响的极端事件和记录值的统计，这是支持数值模拟，我们确定的情况下，漂移可以确定没有相关的随机变量分布的信息。我们的研究结果有助于使用极端事件统计作为相关轨迹中小漂移的信号。
英文摘要：
We analyse extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that for our data the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.
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