Introduction to the non-asymptotic analysis of random matrices
نویسنده
چکیده
2 Preliminaries 7 2.1 Matrices and their singular values . . . . . . . . . . . . . . . . . . 7 2.2 Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sub-gaussian random variables . . . . . . . . . . . . . . . . . . . 9 2.4 Sub-exponential random variables . . . . . . . . . . . . . . . . . . 14 2.5 Isotropic random vectors . . . . . . . . . . . . . . . . . . . . . . . 17 2.6 Sums of independent random matrices . . . . . . . . . . . . . . . 20
منابع مشابه
Non-asymptotic theory of random matrices: extreme singular values
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices w...
متن کاملAsymptotic results on the product of random probability matrices
I study the product of independent identically distributed D × D random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability matrix(asymptotic matrix) in which any two rows are the same. A parameter λ is introduced for the exponential coefficient which can be used to describe the convergent rat...
متن کاملAsymptotic Freeness Almost Everywhere for Random Matrices
Voiculescu’s asymptotic freeness result for random matrices is improved to the sense of almost everywhere convergence. The asymptotic freeness almost everywhere is first shown for standard unitary matrices based on the computation of multiple moments of their entries, and then it is shown for rather general unitarily invariant selfadjoint random matrices (in particular, standard selfadjoint Gau...
متن کاملLow rank perturbations of large elliptic random matrices ∗ Sean O ’ Rourke
We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as w...
متن کاملAsymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data
Kernel density estimators are the basic tools for density estimation in non-parametric statistics. The k-nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paper, we initially introduce the k-nearest neighbor kernel density estimator in the random left-truncatio...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1011.3027 شماره
صفحات -
تاریخ انتشار 2010