Fair Allocations to Random Points
Speaker: Ron Peled, Courant Institute of Mathematical Sciences, NYU
Location: Warren Weaver Hall 1302
Date: Monday, November 2, 2009, 3:45 p.m.
Given an infinite collection of points in space, how do we allocate the same area to each point in a decentralized, shift‐invariant way? Such allocations have been the subject of many investigations in recent years and different approaches to the problem have used such tools as: the Gale‐Shapley stable marriage algorithm, the Riemann mapping theorem and Newtonian gravity. I will survey results in the field, with special focus on the Gradient Flow Allocation, a natural allocation rule suggested by Sodin and Tsirelson, and its variant ‐ the Gravitational Allocation. My own contribution to the subject is joint with Sourav Chatterjee, Yuval Peres and Dan Romik.