英文标题：
《On the overlaps between eigenvectors of correlated random matrices》
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作者：
Jo\\\"el Bun, Jean-Philippe Bouchaud, Marc Potters
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最新提交年份：
2017
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英文摘要：
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum thermalisation to high dimensional statistics. We find that the overlaps only depend on measurable quantities, and do not require the knowledge of the underlying \"true\" (noiseless) matrices. We apply our results to the case of empirical correlation matrices, that allow us to estimate reliably the width of the spectrum of the true correlation matrix, even when the latter is very close to the identity. We illustrate our results on the example of stock returns correlations, that clearly reveal a non trivial structure for the bulk eigenvalues. We also apply our results to the problem of matrix denoising in high dimension.
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中文摘要：
我们得到了加性或乘性噪声下大相关随机矩阵特征向量之间重叠的一般精确公式。这些结果在从量子热化到高维统计的许多不同环境中都有潜在的应用。我们发现重叠只依赖于可测量的量，不需要了解底层的“真”（无噪声）矩阵。我们将我们的结果应用于经验相关矩阵的情况，这使我们能够可靠地估计真实相关矩阵的谱宽，即使后者非常接近恒等式。我们以股票收益率相关性为例说明了我们的结果，这清楚地揭示了大量特征值的非平凡结构。我们还将我们的结果应用于高维矩阵去噪问题。
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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：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：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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