Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 177, Issue 3-4, Pages 1103-1135Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-020-00970-1
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Funding
- Ministerio de Economia y Competitividad [MTM2015-67304-P]
- Russian Science Foundation [18-11-00132] Funding Source: Russian Science Foundation
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We investigate the noise sensitivity of the top eigenvector of a Wigner matrix in the following sense. Let v be the top eigenvector of an NxN Wigner matrix. Suppose that k randomly chosen entries of the matrix are resampled, resulting in another realization of the Wigner matrix with top eigenvector v[k]. We prove that, with high probability, when kMUCH LESS-THANN5/3-o(1), then v and v[k] are almost collinear and when k >> N5/3, then v[k] is almost orthogonal to v.
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