| Description: | [DMS Seminar] Dr. Arijit Chakrabarty (Indian Statistical Institute) -- Random matrices, the Hadamard product and the Free Convolutions |
| Date: | Friday, Sep 16, 2016 |
| Time: | 3 p.m. - 4 p.m. |
| Venue: | 108, Lecture Hall Complex |
| Details: | Random matrices whose entries come from a stationary Gaussian process are studied. It is shown that the limiting spectral distribution is determined by the absolutely continuous component of the spectral measure of the stationary process, a phenomenon resembling that in the situation where the entries of the matrix are i.i.d. On the other hand, the discrete component contributes to the limiting behaviour of the eigenvalues in a completely different way. The random matrix results obtained are used to understand when a free convolution of two measures is absolutely continuous with respect to the Lebesgue measure. It is shown that if the support of a probability measure is contained in the positive half line, and is bounded away from zero, then its free multiplicative convolution with the semicircle law is absolutely continuous. For the proof, a result concerning the Hadamard product of a deterministic matrix and a scaled Wigner matrix is needed. This talk is based on joint works with Rajat Subhra Hazra and Deepayan Sarkar. |
| Calendar: | Seminar Calendar (entered by saugata.bandyopadhyay) |