Chebyshev points have a β(1/2, 1/2) distribution. The generic orbits of the chaotic function 4x(1-x) also have a β(1/2, 1/2) distribution (1), and a large enough finite portion of such an orbit lies very close to the the Chebyshev points: could we use these points in place of Chebyshev points? More generally:

Question: If f:[-1,1] → ℝ is a continuous function and for each integer n, Γ(n) is a random sample of n points from a β (1/2,1/2) distribution on [-1,1] do the Hermite-Fejér polynomials corresponding to the grid points Γ(n) converge uniformly to f with probability 1?

The link http://www.statsci.org/smyth/pubs/EoB/bap064-.pdf is broken.

Regards

## Pablo Angulo Ardoy · 20 Apr, 2019