Asymptotic Distribution of eigenvalues and eigenvectors

Question

Let $\mathbf{A}\in\mathbb{R}^{n\times n}$ be a random matrix. Now consider the following two cases:

1. Suppose $n$ is fixed and is a small number less than 100. If I take sufficiently large samples, N, (N >10000) of $\mathbf{A}$ and find the resultant distribution of the eigenvalues/vectors, can I call it asymptotic or limiting distribution?

2. n is not fixed. If the distribution of eigenvalue/vectors is based on the limit as $n\rightarrow\infty$ and $N\rightarrow\infty$, can I call it asymptotic distribution?

   So, which of the two can be called asymptotic distribution of eigenvalues/vectors?

Answer 1

Both of those are "asymptotic distribution of eigenvalues/vectors".

In one, you are letting the number of samples grow; in the other, you are letting the size of the samples grow.

Different questions which may have different distributions.