Open Access
Translator Disclaimer
2016 Stable transports between stationary random measures
Mir-Omid Haji-Mirsadeghi, Ali Khezeli
Electron. J. Probab. 21: 1-25 (2016). DOI: 10.1214/16-EJP4237


We give an algorithm to construct a translation-invariant transport kernel between two arbitrary ergodic stationary random measures on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an arbitrary ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given a pair of realizations of the two measures. The (non-constructive) existence of such a transport kernel was proved in [9]. Our algorithm is a generalization of the work of [3], in which a construction is provided for the Lebesgue measure and an ergodic simple point process. In the general case, we limit ourselves to what we call constrained transport densities and transport kernels. We give a definition of stability of constrained transport densities and introduce our construction algorithm inspired by the Gale-Shapley stable marriage algorithm. For stable constrained transport densities, we study existence, uniqueness, monotonicity w.r.t. the measures and boundedness.


Download Citation

Mir-Omid Haji-Mirsadeghi. Ali Khezeli. "Stable transports between stationary random measures." Electron. J. Probab. 21 1 - 25, 2016.


Received: 14 April 2015; Accepted: 3 April 2016; Published: 2016
First available in Project Euclid: 5 August 2016

zbMATH: 1346.60068
MathSciNet: MR3539645
Digital Object Identifier: 10.1214/16-EJP4237

Primary: 60G10 , 60G55 , 60G57

Keywords: Allocation , capacity constrained transport kernel , mass transport , Palm distribution , Shift-coupling , Stable matching , Stationary random measure , Voronoi transport kernel


Vol.21 • 2016
Back to Top