A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

摘要

Let Ξ⊂ℝ d be a set of centers chosen according to a Poisson point process in ℝ d . Let ψ be an allocation of ℝ d to Ξ in the sense of the Gale–Shapley marriage problem, with the additional feature that every center ξ∈Ξ has an appetite given by a nonnegative random variable α. Generalizing some previous results, we study large deviations for the distance of a typical point x∈ℝ d to its center ψ(x)∈Ξ, subject to some restrictions on the moments of α.