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Author Bourgade, Paul ♦ Yau, Horng-Tzer ♦ Yin, Jun
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Random Matrix ♦ Local Circular Law ♦ Circular Law ♦ Uniform Measure ♦ Uniform Subexponential Decay Condition ♦ Matrix Entry ♦ Unit Disk ♦ Unit Circle ♦ Symmetry Assumption Converges ♦ Spectral Measure ♦ Local Version ♦ Rescaled Random Matrix
Abstract The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point z away from the unit circle. More precisely, if z − 1 � τ for arbitrarily small τ> 0, the circular law is valid around z up to scale N −1/2+ε for any ε> 0 under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study