A Wegner estimate for Wigner matrices

نویسندگان

  • Anna Maltsev
  • Benjamin Schlein
چکیده

In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of Wigner matrices. The Wegner estimate gives an upper bound for the probability to find an eigenvalue in an interval I, proportional to the size |I| of the interval.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Wegner estimate and level repulsion for Wigner random matrices

We consider N × N Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order 1/N . Under suitable assumptions on the distribution of the single matrix element, we first prove that, away from the spectral edges, the empirical density of eigenvalues concentrates a...

متن کامل

Eigenvalue variance bounds for Wigner and covariance random matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and re...

متن کامل

Statistical Mechanics and Random Matrices

Statistical Mechanics and Random Matrices 3 1. Introduction 6 2. Motivations 7 3. The different scales; typical results 12 Lecture 1. Wigner matrices and moments estimates 15 1. Wigner's theorem 16 2. Words in several independent Wigner matrices 23 3. Estimates on the largest eigenvalue of Wigner matrices 25 Lecture 2. Gaussian Wigner matrices and Fredholm determinants 27 1. Joint law of the ei...

متن کامل

Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation

We consider N ×N Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance N for some positive β > 0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel. AMS Subject Classification: 15A52, 82B44 Running title: Universality for Wigner matrices

متن کامل

Localization and Absence of Breit-wigner Form for Cauchy Random Band Matrices

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index μ = 1/2 and the characteristic energy scale α is strongly enhanced as compared to the Breit-Wigner width. The unperturbed eigenstates decay according to the non-exponential ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011