= Centered truncation of a Wigner matrix
{title2=$\widehat X_{ij}=N^{-1/2}(Y_{ij}\mathbf1_{|Y_{ij}|<C}-\mathbb E[Y_{ij}\mathbf1_{|Y_{ij}|<C}])$}
Truncate the unscaled entries of a <Wigner matrix> at a fixed threshold and subtract their <expected values>. The difference between original and truncated entries is $N^{-1/2}(Z_C-\mathbb EZ_C)$ with $Z_C=Y\mathbf1_{|Y|\geq C}$, so its <variance> is bounded by $N^{-1}\mathbb E[Y^2\mathbf1_{|Y|\geq C}]$. The centering term cannot be discarded for an asymmetric entry law.
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