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Central limit theorems for radial random walks on matrices for
-
Michael Voit
Published/Copyright:
March 27, 2012
Abstract.
Let 
be a fixed probability measure.
For each dimension 
, let 
be
i.i.d. 
-valued radial random variables with
radial distribution 
. We derive two central limit theorems (CLTs) for
for 
with normal limits. The first CLT for 
follows from
known estimates of convergence in the CLT on 
,
while the second CLT for 
will be a consequence of asymptotic properties of Bessel convolutions.
Both limit theorems are considered also for 
-invariant random walks on the space of 
matrices instead of 
for 
and fixed dimension 
.
Keywords.: Radial random walks; central limit theorems; random matrices; large dimensions; matrix cones; Bessel convolution; Bessel functions of matrix argument
Received: 2011-09-08
Accepted: 2012-02-10
Published Online: 2012-03-27
Published in Print: 2012-April
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Radial random walks;
central limit theorems;
random matrices;
large dimensions;
matrix cones;
Bessel convolution;
Bessel functions of matrix argument
Articles in the same Issue
- Masthead
- Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle
- A priori estimates of Nodal solutions on the annulus for some PDE and their Morse index
- Combined Sundman–Darboux transformations and solutions of nonlinear ordinary differential equations of second order
- Multiresolution analysis on local fields and characterization of scaling functions
- Multiplicity of positive solution of -Laplacian problems with sign-changing weight functions
- Small gaps Fourier series and generalized variations
- Central limit theorems for radial random walks on matrices for
