Yuktibhasa seminar series
Title: Optimal transport of random points.
Abstract: What is the cost of matching a grid or transporting Lebesgue measure to a point process, i.e., a collection of random points? Since the work of Ajtai, Komlós, and Tusnády in the 1980s, the study of matching and transportation costs has garnered significant attention, particularly for i.i.d. random points. The question has interested researchers in computer science, probability, statistics, PDE and optimal transport theory. A key finding is the striking dimension-dependent transition: in dimensions higher than two, the L^2-matching cost with a grid is finite, whereas in two dimensions, even the L^1-matching cost is infinite. In the last part, we shall discuss extensions to general point processes. The last part is based on a joint work with Raphael Lachieze-Rey.
