标题： 广义变形Ginibre系综的极限特征值分布 显示英文标题

标题： Limiting eigenvalue distribution of the general deformed Ginibre ensemble

摘要： Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. 我们研究$X_n$的极限特征值分布。 在 arXiv:0807.4898 中显示，$X_n$的特征值分布收敛到某个确定性测度。 该测度对于情况$A_n=0$是已知的。 在$A_n$的一些一般收敛条件下，我们证明了极限测度密度的公式。 我们还得到了分布收敛速度的估计。 这里使用的方法基于超对称积分。 显示英文摘要

摘要： Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. We study the limiting eigenvalue distribution of $X_n$. In arXiv:0807.4898 it was shown that the eigenvalue distribution of $X_n$ converges to some deterministic measure. This measure is known for the case $A_n=0$. Under some general convergence conditions on $A_n$ we prove a formula for the density of the limiting measure. We also obtain an estimation on the rate of convergence of the distribution. The approach used here is based on supersymmetric integration.