Fermionic eigenvector moment flow
成果类型：
Article
署名作者：
Benigni, Lucas
署名单位：
Universite Paris Cite
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-020-01018-0
发表日期：
2021
页码：
733-775
关键词：
摘要：
We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow (Bourgade and Yau in Commun Math Phys 350(1):231-278, 2017). These observables can be seen as a Fermionic counterpart to the original (Bosonic) ones. By analyzing both Fermionic and Bosonic observables, we obtain new correlations between eigenvectors: (i) The fluctuations n-ary sumation Sigma(alpha is an element of I)|uk(alpha)|2-|I|/N decorrelate for distinct eigenvectors as the dimension N grows. (ii) An optimal estimate on the partial inner product n-ary sumation Sigma(alpha is an element of I) u(k)(alpha)(u(l)) over bar (alpha) between two eigenvectors is given. These static results obtained by integrable dynamics are stated for generalized Wigner matrices and should apply to wide classes of mean field models.
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