We consider a dilute version of the Wigner ensemble of n-dimensional randommatrices H such that each row has in average \rho_n non-zero elements. We studyasymptotic properties of the spectral norm of H on the scale n^{-2/3} in thelimit when \rho_n is of the order n^{-2/3(1+\epsilon)} with \epsilon >0.
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