Spectral properties of polynomials in independent Wigner and deterministic matrices

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spectral Properties of Random and Deterministic CMV Matrices

The CMV matrices are unitary analogues of the discrete one-dimensional Schrödinger operators. We review spectral properties of a few classes of CMV matrices and describe families of random and deterministic CMV matrices which exhibit a transition in the distribution of their eigenvalues.

متن کامل

The norm of polynomials in large random and deterministic matrices

Let XN = (X (N) 1 , . . . , X (N) p ) be a family of N × N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices YN = (Y (N) 1 , . . . , Y (N) q ), possibly random but independent of XN , for which the operator norm of P (XN ,YN ,Y∗ N) converges almost surely for all polynomials P . Limits are described by operator norms of object...

متن کامل

High Moments of Large Wigner Random Matrices and Asymptotic Properties of the Spectral Norm

We consider the Wigner ensemble of n×n real symmetric random matrices of the form A (n) ij = 1 √ n aij , whose entries {aij}1≤i≤j≤n are independent random variables with the same symmetric probability distribution such that Eaij = v , and study the corresponding ensemble of random matrices with truncated random variables  (n) ij = 1 √ n â (n) ij , where âij = aijI[−Un,Un](aij). Our main result...

متن کامل

A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices

Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from one of the recent papers of Erdös-Yau-Yin. We also use an algebraic description of the law of the anticommutator of free semicircular variables due to Nica-Speicher, a self-adjointnes...

متن کامل

Asymptotic expansion of the expected spectral measure of Wigner matrices

We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We interpret this expansion as the moments of the addition of the semicircle law and 1/n times an explicit signed measured with null total mass. This signed measure depends only on the second and fourth moments of the ent...

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

ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2017

ISSN: 0022-1236

DOI: 10.1016/j.jfa.2017.07.010