[HTML][HTML] Eigenvectors of random matrices: a survey
Journal of Combinatorial Theory, Series A, 2016•Elsevier
… Although this survey examines several models of random matrices, we mostly focus on
Wigner matrices, specifically Wigner matrices whose atom variables have light tails (eg sub-exponential
atom variables). In this case, the main message we would like to communicate is that an …
For comparison, we also discuss other models of random matrices, such as heavy-tailed
and band random matrices, whose eigenvectors do not behave like random vectors
uniformly distributed on the unit sphere. … In Section 8 and Section 9, we discuss results …
Wigner matrices, specifically Wigner matrices whose atom variables have light tails (eg sub-exponential
atom variables). In this case, the main message we would like to communicate is that an …
For comparison, we also discuss other models of random matrices, such as heavy-tailed
and band random matrices, whose eigenvectors do not behave like random vectors
uniformly distributed on the unit sphere. … In Section 8 and Section 9, we discuss results …
Abstract
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random.
Elsevier
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