Gravitational allocation to Poisson points

By Sourav Chatterjee, Ron Peled, Yuval Peres, Dan Romik. 2006

56 citations recorded by the source corpus.

For d ≥ 3, we construct a non-randomized, fair and translationequivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R d , defined by allocating to each of the Poisson points its basin of attraction with respect to the flow induced by a gravitational force field exerted by the points of the Poisson process. We prove that this allocation rule is economical in the sense that the allocation diameter, defined as the diameter X of the basin of attraction containing the origin, is a random variable with a rapidly decaying tail. Specifically, we have the tail bound P(X > R) ≤ C exp h − cR(logR) αd i

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c9f745bb8a89a1b0bb819c96f1152a286a44139

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In Applied Mathematics

In Finance

In Mathematical Physics

Citations in the corpus

Invariant transports of stationary random measures and mass-stationarity (2009, background): “) Triggered by Liggett’s paper, invariant transports of the Lebesgue measure on R (or of the counting measure on Z ) to an ergodic point process of intensity 1 have received considerable attention in recent years (see [3, 9, 11, 14]).”
Optimal transport from Lebesgue to Poisson (2010, background): “t process [13]. One of the challenges is to produce allocations with fast decay of the distance of a typical point in a cell to its center or of the diameter of the cell. The gravitational allocation [8, 9] in d≥3 was the ﬁrst allocation with exponential decay. Moreover, all the cells are connected ”