英文标题：
《Record statistics of a strongly correlated time series: random walks and
L\\\'evy flights》
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作者：
Claude Godreche, Satya N. Majumdar, Gregory Schehr
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最新提交年份：
2017
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英文摘要：
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\\\'evy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful \"laboratory\" to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e., the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.
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中文摘要：
我们回顾了强相关时间序列记录统计的最新进展，其条目表示一条直线上随机游动或列维飞行的位置。在简要回顾了独立同分布随机变量的记录理论之后，我们重点讨论了随机游动。在过去的几年里，人们确实意识到随机游动是一个非常有用的“实验室”，可以测试相关性对记录统计数据的影响。我们从具有对称跳跃（连续和离散）的简单一维随机游动开始，详细讨论了记录数量的统计信息，以及记录的年龄，即两个连续破纪录事件之间的时间间隔。然后，我们回顾了各种随机游动模型的结果，包括具有线性漂移的随机游动、连续时间随机游动、约束随机游动（如随机游动桥）和多个独立随机游动者的情况。最后，我们讨论了与记录相关的进一步观察值，如记录增量，以及记录统计的物理应用引起的一些问题，如测量误差和噪声的影响。
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分类信息：

一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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