Abstract
We show that the spectral radius of an N× N random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by 2 σ + o(N−6/11+ε), where σ2 is the variance of the matrix entries and ε is an arbitrary small positive number. Our bound improves the earlier results by Z. Füredi and J. Komlós (1981), and Van Vu (2005).
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Péché, S., Soshnikov, A. Wigner Random Matrices with Non-Symmetrically Distributed Entries. J Stat Phys 129, 857–884 (2007). https://doi.org/10.1007/s10955-007-9340-y
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DOI: https://doi.org/10.1007/s10955-007-9340-y