Abstract
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
.