For some families of random hertmitian matrices $X_n$ with eigenvalues $\lambda_1,\dots, \lambda_n$, their random spectral measures $\mu_n(\cdot) =\sum_{j=1}^n 1_{\lambda_j\in (\cdot)}$ can be approximated, with probability one, by a sequence of deterministic measures $\nu_n$ as the dimension of the matrix $n\to\infty$.

I will give examples of results of this type by several authors in classical probability. One notable feature of these theorems is complete absence of free probability.

My goal is to present a formulation of the "principle of deterministic equivalence" that is too narrow to be universally true but that still covers non-trivial cases. Its advantage for a practitioner of classical probability is that it can be freed from free probability.

This talk was inspired by discussions with Jack W. Silverstein.