Average density of states for Hermitian Wigner matrices

Anna V Maltsev, Benjamin Schlein

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


We consider ensembles of N×N Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as N tends to infinity.
Original languageEnglish
Pages (from-to)2797-2836
Number of pages40
JournalAdvances in Mathematics
Issue number5
Publication statusPublished - 1 Dec 2011


  • Wignerʼs semicircle law;


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