Rutgers Discrete Mathematics Seminar

Title: Optimal local semi-circle law and delocalization property of eigenvectors

Speaker: Ke Wang, Rutgers University

Date: Tuesday, April 24, 2012 2:00pm

Location: Hill Center, Room 124, Rutgers University, Busch Campus, Piscataway, NJ


Consider $n times n$ Hermitian random matrices $M_n$ with i.i.d entries with mean zero, variance one and bounded high moments. I will discuss the recent progress in studying the eigenvalue statistics at small scales, especially the local semi-circle law. In joint work with Van Vu, we are able to prove the local semi-circle law for $frac{1}{sqrt{n}} M_n$ on the scale of $log n/ n$. As a consequence, we can show that any unit eigenvector, whose eigenvalue is bounded away from the spectral edges, is delocalized in the sense that the infinity norm has upper bound $sqrt{log n/n}$.