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SUMMARY:Asymptotics of Eigenvectors and Eigenvalues for Large Structured R
 andom Matrices - Jinchi Lv (University of Southern California)
DTSTART:20180628T130000Z
DTEND:20180628T134500Z
UID:TALK107491@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Characterizing the exact asymptotic distributions of high-dime
 nsional eigenvectors for large structured random matrices poses important 
 challenges yet can provide useful insights into a range of applications. T
 his paper establishes the asymptotic properties of the spiked eigenvectors
  and eigenvalues for the generalized Wigner random matrix\, where the mean
  matrix is assumed to have a low-rank structure. Under some mild regularit
 y conditions\, we provide the asymptotic expansions for the spiked eigenva
 lues and show that they are asymptotically normal after some normalization
 . For the spiked eigenvectors\, we provide novel asymptotic expansions for
  the general linear combination and further show that the linear combinati
 on is asymptotically normal after some normalization\, where the weight ve
 ctor can be an arbitrary unit vector. Simulation studies verify the validi
 ty of our new theoretical results. Our family of models encompasses many p
 opularly used ones such as the stochastic block models with or without ove
 rlapping communities for network analysis and the topic models for text an
 alysis\, and our general theory can be exploited for statistical inference
  in these large-scale applications. This is a joint work with Jianqing Fan
 \, Yingying Fan and Xiao Han.
LOCATION:Seminar Room 1\, Newton Institute
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