Abstract: The problems of sampling and interpolation concern the relation between functions in a given class and their values on a distinguished set (samples). The two main questions are: Is every function determined by its samples? Can a function with prescribed samples be found?
A random point process is repulsive if the statistics of disjoint observation regions are negatively correlated. As a consequence of repulsion, a typical realization of such a process is better distributed than a Poissonian one.
I will present classical and recent results on sampling and interpolation, and discuss why repulsive point processes are often good candidates to solve both problems. As a case in point, I will focus on the planar Coulomb gas (Boltzmann-Gibbs distribution) and investigate its statistics at low temperatures by means of sampling and interpolation properties for weighted polynomials.

https://univienna.zoom.us/j/69609892626?pwd=R2E1ZDdnRmdubGl1VzZXZ2dGd0xEUT09