10.1214/17-EJP38
Nemish, Yuriy
Yuriy
Nemish0000-0002-7327-856X
Local law for the product of independent non-Hermitian random matrices with independent entries
Institute of Mathematical Statistics
2017
2018-12-11T11:49:44Z
2019-01-24T13:00:09Z
journal_article
https://research-explorer.app.ist.ac.at/record/1023
https://research-explorer.app.ist.ac.at/record/1023.json
10836489
742275 bytes
application/pdf
We consider products of independent square non-Hermitian random matrices. More precisely, let X1,…, Xn be independent N × N random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed that the empirical spectral distribution of the product of n random matrices with iid entries converges to (equation found). We prove that if the entries of the matrices X1,…, Xn are independent (but not necessarily identically distributed) and satisfy uniform subexponential decay condition, then in the bulk the convergence of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.