Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5129695 | Statistics & Probability Letters | 2017 | 8 Pages |
Abstract
It is shown that if a probability measure ν is supported on a closed subset of (0,â), that is, its support is bounded away from zero, then the free multiplicative convolution of ν and the semicircle law is absolutely continuous with respect to the Lebesgue measure. For the proof, a result concerning the Hadamard product of a deterministic matrix and a scaled Wigner matrix is proved and subsequently used. As a byproduct, a result, showing that the limiting spectral distribution of the Hadamard product is same as that of a symmetric random matrix with entries from a mean zero stationary Gaussian process, is obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Arijit Chakrabarty,