A note on large deviations for the stable marriage of Poisson and Lebesgue with random appetites

Let $\Xi\subset\mathbb R^d$ be a set of centers chosen according to a Poisson point process in $\mathbb R^d$. Let $\psi$ be an allocation of $\mathbb R^d$ to $\Xi$ in the sense of the Gale-Shapley marriage problem, with the additional feature that every center $\xi\in\Xi$ has an appetite given by a nonnegative random variable $\alpha$. Generalizing some previous results, we study large deviations for the distance of a typical point $x\in\mathbb R^d$ to its center $\psi(x)\in\Xi$, subject to some restrictions on the moments of $\alpha$.