Probability that product of real random matrices have all eigenvalues real tend to 1

Tulasi Ram Reddy

Statistics & Probability Letters, 2017, vol. 124, issue C, 30-32

Abstract: In this note we consider products of real random matrices with fixed size with all entries as i.i.d. random variables. The product of such matrices has all eigenvalues real, with high probability. In other words, let X1,X2,… be i.i.d. k×k real matrices, whose entries are independent and identically distributed from probability measure μ. Let An=X1X2…Xn. Then it is conjectured that P(Anhasallrealeigenvalues)→1asn→∞. We show that the conjecture is true when μ has an atom.

Keywords: Random matrices; Products of random matrices; Real eigenvalues (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521730007X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:124:y:2017:i:c:p:30-32

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2016.12.021

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().