The smallest singular value of large random rectangular Toeplitz and circulant matrices

Alexei Onatski, Vladislav Kargin

Let $x_i$, $i\in \mathbb{Z}$ be a sequence of i.i.d. standard normal random variables. Consider rectangular Toeplitz $\mathbf{X}={\left(x_{j-i}\right)}_{1\le i\le p,1\le j\le n}$…