Concentration of the Spectral Measure for Large Random Matrices with Stable Entries

نویسنده

  • Christian Houdré
چکیده

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value. AMS 2000 Subject Classification: 60E07, 60F10, 15A42, 15A52

برای دانلود 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

Concentration of the Spectral Measure of Large Wishart Matrices with Dependent Entries

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

متن کامل

ar X iv : 0 81 0 . 27 53 v 1 [ m at h . ST ] 1 5 O ct 2 00 8 Concentration of the spectral measure of large Wishart matrices with dependent entries

We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

متن کامل

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

متن کامل

Spectral Measure of Heavy Tailed Band and Covariance Random Matrices

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure μ̂ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N ×N symmetric matrix YσN whose (i, j) entry is σ( i N , j N )xij where (xij , 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007