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On the Universality of the Non-singularity of General Ginibre and Wigner Random Matrices

Hold Date
2016-09-26 16:00〜2016-09-26 17:30
Seminar Room W1-D-725, West Zone 1, Ito campus, Kyushu University
Object person
Rahul Roy (Indian Statistical Institute)

We study the universal asymptotically almost sure non-singularity of general Ginibre and 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 and not on the range of values of the random entries.

This lecture is based on Manrique, Perez-Abreu and Roy (2016, Random matrices Theory And Application).