ABSTRACT
Triangular random matrices have gained importance recently. For example, Dykema and Haagerup (2004)[52] were led to the consideration of the following asymmetric triangular version of the Wigner matrix T n = t 1 , 1 t 1 , 2 t 1 , 3 … t 1 , n - 1 t 1 , n 0 t 2 , 2 t 2 , 3 … t 2 , n - 1 t 2 , n 0 0 t 3 , 3 … t 3 , n - 1 t 3 , n ⋮ 0 0 0 … 0 t n , n $$ \begin{aligned} T_{n}\ = \left[ \begin{array} {cccccc} t_{1,1}&t_{1,2}&t_{1,3}&\ldots&t_{1,n-1}&t_{1,n} \\ 0&t_{2,2}&t_{2,3}&\ldots&t_{2,n-1}&t_{2,n} \\ 0&0&t_{3,3}&\ldots&t_{3,n-1}&t_{3,n} \\&\,&\vdots&\,&\\ 0&0&0&\ldots&0&t_{n,n} \end{array} \right] \end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/math8_1.tif"/>
