Stable Marriage of Poisson and Lebesgue

Опубликовано 6 сентября 2016, 4:56

Given a point process M of intensity one in the plane, the well-known Voronoi tesselation assigns a polygon (of different area) to each point of M. The geometry of fair allocations (assigning unit area to each point of M) is richer and more mysterious: see math.ubc.ca/~holroyd/stable.ht... There is a unique fair allocation that is stable in the sense of the Gale-Shapley stable marriage problem, every point of M is assigned a bounded region with finitely many components, but obtaining any(!) tail estimate for the diameter of these regions is open. These allocations arose from the continuum version of the extra