Delocalization of eigenvectors of random matrices with independent entries.(English)Zbl 1352.60007

Summary: We prove that an $$n\times n$$ random matrix $$G$$ with independent entries is completely delocalized. Suppose that the entries of $$G$$ have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high probability all unit eigenvectors of $$G$$ have all coordinates of magnitude $$O(n-1/2)$$, modulo logarithmic corrections. This comes as a consequence of a new, geometric approach to delocalization for random matrices.

MSC:

 60B20 Random matrices (probabilistic aspects) 15B52 Random matrices (algebraic aspects)
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References:

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