On Empirical Spectral Distributions for Random Tensor Product Models

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in the early literature, while preserving the original conclusions. Empirical spectral distributions of covariance matrices are key for understanding the data, and their almost sure convergence is oftentimes desirable. The random tensor product model, $X=(x_{i_1}x_{i_2}...x_{i_d})_{1 \leq i_1