| Citation key |
BB-Distribution-Of-The-Eigenvalues-Of-A-Random-System-Of-Homogeneous-Polynomials |
| Author |
Paul Breiding and Peter Bürgisser |
| Pages |
88-107 |
| Year |
2016 |
| DOI |
10.1016/j.laa.2016.02.020 |
| Journal |
Linear Algebra and its Applications |
| Volume |
497 |
| Month |
05 |
| Abstract |
Let $f=(f_1,..,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call λ ∈ $\mathbb C$ an eigenvalue of $f$ if there exists a nonzero $v$ ∈ $\mathbb C$ with $f(v)=$ λ $v$, generalizing the case of eigenvalues of matrices ($d=1$). We derive the distribution of λ when the $f_i$ are independently chosen at random according to the unitary invariant Weyl distribution and determine the limit distribution for $n\to\infty$. |
