Heavy-tailed random matrices
2009
We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant influence on the statistics. They also completely change universal properties of eigenvalues and eigenvectors of random matrices. We concentrate here on the universal macroscopic properties of (1) Wigner matrices belonging to the Levy basin of attraction, (2) matrices representing stable free random variables and (3) a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles.
Keywords:
- Random element
- Circular law
- Multivariate random variable
- Convolution of probability distributions
- Sum of normally distributed random variables
- Algebra of random variables
- Random matrix
- Heavy-tailed distribution
- Mathematical analysis
- Statistics
- Mathematics
- Combinatorics
- Convergence of random variables
- Statistical physics
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