6 - Empirical Christoffel–Darboux Analysis

Summary

For empirical measures supported on a random sample, statistical bounds describe the large-sample asymptotic behavior of the empirical Christoffel function. The Christoffel function associated with a fixed degree will converge to its population counterpart in the large-sample limit. The convergence can be made quantitative using random matrix concentration. Furthermore, in the context of singularly supported population measure, the rank will stabilize almost surely for a finite number of samples.