Brown measure and asymptotic freeness of elliptic and related matrices
2019 ◽
Vol 08
(02)
◽
pp. 1950007
We show that independent elliptic matrices converge to freely independent elliptic elements. Moreover, the elliptic matrices are asymptotically free with deterministic matrices under appropriate conditions. We compute the Brown measure of the product of elliptic elements. It turns out that this Brown measure is same as the limiting spectral distribution.
1995 ◽
Vol 54
(2)
◽
pp. 295-309
◽
2014 ◽
Vol 03
(04)
◽
pp. 1450015
◽
1998 ◽
Vol 5
(2)
◽
pp. 423-432
2013 ◽
Vol 44
(5)
◽
pp. 695-710
2013 ◽
Vol 28
(2)
◽
pp. 745-783
◽
2002 ◽
Vol 60
(1)
◽
pp. 111-120
◽
2007 ◽
Vol 98
(6)
◽
pp. 1099-1122
◽
2010 ◽
Vol 101
(10)
◽
pp. 2434-2451
◽
Keyword(s):