article
Local law for the product of independent non-Hermitian random matrices with independent entries
published
yes
Yuriy
Nemish
author 4D902E6A-F248-11E8-B48F-1D18A9856A870000-0002-7327-856X
LaEr
department
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.
https://research-explorer.ista.ac.at/download/1023/5149/IST-2017-802-v1+1_euclid.ejp.1487991681.pdf
application/pdfno
Institute of Mathematical Statistics2017
eng
Electronic Journal of Probability
10836489
00039661190002210.1214/17-EJP38
22
Nemish Y. Local law for the product of independent non-Hermitian random matrices with independent entries. <i>Electronic Journal of Probability</i>. 2017;22. doi:<a href="https://doi.org/10.1214/17-EJP38">10.1214/17-EJP38</a>
Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2017. <a href="https://doi.org/10.1214/17-EJP38">https://doi.org/10.1214/17-EJP38</a>.
Nemish Y. 2017. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 22, 22.
Nemish, Y. (2017). Local law for the product of independent non-Hermitian random matrices with independent entries. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/17-EJP38">https://doi.org/10.1214/17-EJP38</a>
Y. Nemish, “Local law for the product of independent non-Hermitian random matrices with independent entries,” <i>Electronic Journal of Probability</i>, vol. 22. Institute of Mathematical Statistics, 2017.
Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” <i>Electronic Journal of Probability</i>, vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:<a href="https://doi.org/10.1214/17-EJP38">10.1214/17-EJP38</a>.
Y. Nemish, Electronic Journal of Probability 22 (2017).
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