JSM 2003 Online Program

Abstract #302254

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Activity Number:	8
Type:	Invited
Date/Time:	Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor:	IMS
Abstract - #302254
Title:	Stable Marriage of a Poisson Process to Lebesgue Measure
Author(s):	Yuval Peres*+
Companies:	University of California
Address:	Statistics Dept., Berkeley, CA, 94720-0001,
Keywords:	Poisson ; Voronoi ; stable
Abstract:	In their classic 1962 paper, Gale and Shapley showed the existence of a perfect matching between n men and n women, which is stable in the sense that there is no man and woman that prefer each other to their assigned mates. We describe a stochastic geometry version of this, where points of a Poisson point process are assigned disjoint sets of unit area in a translation invariant and stable way; here preference is determined by distance. This model exhibits phase transitions and long range order. The problem of uniqueness of the stable partition is related to electrical resistance estimates for certain graphs on the Poisson point process.

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