| Description: | [DMS Seminar] Dr. Indrajit Jana (Temple University, USA) -- Spectrum of Random Band Matrices |
| Date: | Thursday, Aug 02, 2018 |
| Time: | 4 p.m. - 5 p.m. |
| Venue: | G09, Lecture Hall Complex |
| Details: | Random matrix theory can be used as a mathematical tool in several scientific research including Nuclear Physics, Signal Processing, Numerical linear algebra etc. We consider the limiting spectral distribution of matrices of the form $\f{1}{2b_{n}+1} (R + X)(R + X)^{*}$, where $X$ is an $n\times n$ random band matrix of bandwidth $b_{n}$ and $R$ is a non random band matrix of bandwidth $b_{n}$. We show that the Stieltjes transform of ESD of such matrices converges to the Stieltjes transform of a non-random measure; and the limiting Stieltjes transform satisfies an integral equation. For $R=0$, the integral equation yields the Stieltjes transform of the Marchenko-Pastur law. |
| Calendar: | Seminar Calendar (entered by sushil.gorai) |