Normal fluctuation in quantum ergodicity for Wigner matrices
Normal fluctuation in quantum ergodicity for Wigner matrices
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DOI：
10.1214/21-aop1552
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发表时间：
2021-03
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影响因子：
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通讯作者：
Giorgio Cipolloni;L'aszl'o ErdHos;Dominik Schroder
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文献类型：
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作者：
Giorgio Cipolloni;L'aszl'o ErdHos;Dominik Schroder
我们考虑一般确定性矩阵关于N×N维格纳矩阵特征向量的二次型，并证明在大N极限下，它的每个体特征向量都具有高斯波动。证明是[24]启发的Dyson Brown运动的能量方法和我们最近的多预解局部定律[11]的组合。
We consider the quadratic form of a general deterministic matrix on the eigenvectors of an N×N Wignermatrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the largeN limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by [24] and our recent multi-resolvent local laws [11].