Percolation for the stable marriage of Poisson and Lebesgue with random appetites

Abstract

Let Ξ be a set of centres chosen according to a Poisson point process in . Consider the allocation of to Ξ which is stable in the sense of the Gale–Shapley marriage problem, with the additional feature that every centre has a random appetite , where is a non-negative scale constant and V is a non-negative random variable. Generalizing previous results by Freire et al. (Stoch. Proc. Appl. 117(4) (2007), pp. 514–525), we show the absence of percolation when is small enough, depending on certain characteristics of the moment of V.

Keywords:

• Poisson process
• percolation
• stable marriage
• random appetite

Acknowledgements

The author is grateful to the referees for their valuable suggestions and acknowledges the support of CAPES during his research. He wants to thank Carolina Hernández and Juan Sáenz for their independent proof-reading and style suggestions, he also thanks Angélica María Vega for her timely and valuable comments.