Kutatás

2022. április 20., 16:21

Abstract: Consider two infinite random discrete sets of points in the Euclidean space whose distributions are invariant under isometries. Find a perfect matching between them that makes the distance between pairs decay as fast as possible (in the proper sense). Our setup will be when the random point sets are given by Poisson point processes, and we are interested in factor matching rules, meaning that every point can determine its pair using local information and using the same method. In the talk we will introduce all the necessary notions and present the recent solution to the above problem. We will see how the solution is connected to a land-division problem and to the question of whether it is possible to cut a disc of unit area into finitely many pieces and reassemble a unit square from these pieces.