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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_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@
...