--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Yuriy foaf_name: Nemish, Yuriy foaf_surname: Nemish foaf_workInfoHomepage: http://www.librecat.org/personId=4D902E6A-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-7327-856X bibo_doi: 10.1214/17-EJP38 bibo_volume: 22 dct_date: 2017^xs_gYear dct_identifier: - UT:000396611900022 dct_isPartOf: - http://id.crossref.org/issn/10836489 dct_language: eng dct_publisher: Institute of Mathematical Statistics@ dct_title: Local law for the product of independent non-Hermitian random matrices with independent entries@ ...