--- _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' ...