Theoretical Statistics and Mathematics Unit, ISI Delhi

May 7, 2014 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Rahul Roy,
Indian Statistical Institute, Delhi

Title:
Non-singularity of symmetric random matrices

Abstract of Talk

We obtain the almost sure non-singularity of general Wigner
ensembles of random matrices when the distribution of the
entries are independent but not necessarily identically
distributed and may depend on the size of the matrix. These
models include adjacency matrices of random graphs and also
sparse, generalized, universal and banded random
matrices. We find universal rates of convergence and precise
estimates for the probability of singularity which depend only
on the size of the biggest jump of the distribution functions
governing the entries of the matrix. Our proofs are based on
a concentration function inequality due to Kesten and allows
us to improve the known rates of convergence for the Wigner
case when the distribution of the entries do not depend on the
size of the matrix.
This is joint work with Paulo Manrique and Victor P\'{e}rez-Abreu.