Matrix Deviation Inequality for ${\mathrm{\ell }}_p$-Norm

Motivated by the general matrix deviation inequality for i.i.d ensemble Gaussian matrix, we study its universality property. As a starting point for this problem, we show that this property holds for ${\mathrm{\ell }}_p$-norm with $1\leq p< \infty$ and i.i.d ensemble sub-Gaussian random matrix, which is a random matrix with i.i.d mean-zero, unit variance, sub-Gaussian entries.