论文标题
自相与元件和椭圆元件总和的棕色度量
The Brown measure of the sum of a self-adjoint element and an elliptic element
论文作者
论文摘要
我们完全确定了自相邻元素和椭圆元件总和的棕色度量，这是随机矩阵的限制特征值分布 \ [y_n+\ sqrt {s- \ frac {t} {2}} x_n+i \ sqrt {\ frac {\ frac {t} {2}} x_n'\] 其中$ y_n $是$ n \ times n $确定性的Hermitian矩阵，其特征值分布收敛为$ n \ to \ infty $和$ x_n $，$ x_n $和$ x_n'$是独立的高斯单位合并。我们还研究了这种棕色措施的各种渐近行为，因为椭圆元素的方差接近无穷大。
We completely determine the Brown measure of the sum of a self-adjoint element and an elliptic element, which is the limiting eigenvalue distribution of the random matrix \[Y_N+\sqrt{s-\frac{t}{2}}X_N+i\sqrt{\frac{t}{2}}X_N'\] where $Y_N$ is an $N\times N$ deterministic Hermitian matrix whose eigenvalue distribution converges as $N\to\infty$ and $X_N$ and $X_N'$ are independent Gaussian unitary ensembles. We also study various asymptotic behaviors of this Brown measure as the variance of the elliptic element approaches infinity.
