论文标题
稀疏复杂高斯矩阵的可逆性
Invertibility of Sparse Complex Gaussian Matrices
论文作者
论文摘要
令$σ_n（\ cdot）$表示$ n \ times n $矩阵的最小值。众所周知，如果从$ n \ times n $矩阵和$ n $矩阵和$ \ mathbb {p} [p} [p} [p} [p} [σ_n（v vareps \ vareps）中，$ \ mathbb {p} [σ_n（a）\ le \ varepsilon] \ le \ lepsilon n $如果$ a $ n^2 $如果$ a $是从复杂的Ginibre合奏中汲取的。在本文中，对于稀疏的随机矩阵，我们将显示出类似的现象。
Let $σ_n(\cdot)$ denote the least singular value of a $n \times n$ matrix. It is well-known that $\mathbb{P}[σ_n(A) \le \varepsilon] \le \varepsilon n$ if $A$ is drawn from the real Ginibre ensemble of $n \times n$ matrices and $\mathbb{P}[σ_n(A) \le \varepsilon] \le \varepsilon^2 n^2$ if $A$ is drawn from the complex Ginibre ensemble. In this paper, we will show a similar phenomenon occurs for sparse random matrices.
