Abstract: In the beginning of the XXth century, Ornstein and Zernike predicted the sharp behaviour of the two-point function in high temperature/low density systems by formulating a, now famous, heuristic on the structure of correlation functions.
In this talk, I will review the many progresses in the rigorous understanding of this prediction and of its universality. The first part will be a review of the problem and of the current research status, while the second will focus on recent progresses towards the universality question in the framework of percolation models.
The first part will be based on the work of many people -too many to list them here-, while the second will be mostly focused on https://arxiv.org/abs/2009.12054.