---
_id: '1023'
abstract:
- lang: eng
text: 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.
article_number: '22'
article_processing_charge: No
author:
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Nemish Y. Local law for the product of independent non-Hermitian random matrices
with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38
apa: Nemish, Y. (2017). Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/17-EJP38
chicago: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian
Random Matrices with Independent Entries.” Electronic Journal of Probability.
Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38.
ieee: Y. Nemish, “Local law for the product of independent non-Hermitian random
matrices with independent entries,” Electronic Journal of Probability,
vol. 22. Institute of Mathematical Statistics, 2017.
ista: Nemish Y. 2017. Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. 22, 22.
mla: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random
Matrices with Independent Entries.” Electronic Journal of Probability,
vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.
short: Y. Nemish, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:44Z
date_published: 2017-02-06T00:00:00Z
date_updated: 2023-09-22T09:27:51Z
day: '06'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/17-EJP38
external_id:
isi:
- '000396611900022'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:29Z
date_updated: 2018-12-12T10:15:29Z
file_id: '5149'
file_name: IST-2017-802-v1+1_euclid.ejp.1487991681.pdf
file_size: 742275
relation: main_file
file_date_updated: 2018-12-12T10:15:29Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '02'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Probability
publication_identifier:
issn:
- '10836489'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6370'
pubrep_id: '802'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law for the product of independent non-Hermitian random matrices with
independent entries
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 22
year: '2017'
...