Transportation of diffuse random measures on Rd

Günter Last*, Hermann Thorisson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider two jointly stationary and ergodic random measures ξ and η on Rd with equal finite intensities, assuming ξ to be diffuse (non-atomic). An allocation is a random mapping taking Rd to Rd ∪ {∞} in a translation invariant way. We construct allocations transporting the diffuse ξ to arbitrary η, under the mild condition of existence of an 'auxiliary' point process which is needed only in the case when η is diffuse. When that condition does not hold we show by a counterexample that an allocation transporting ξ to η need not exist.

Original languageEnglish
Pages (from-to)577-592
Number of pages16
JournalAlea (Rio de Janeiro)
Issue number1
Publication statusPublished - 1 Jan 2023

Bibliographical note

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© 2023, Alea (Rio de Janeiro). All Rights Reserved.

Other keywords

  • invariant allocation
  • invariant transport
  • Palm measure
  • point process
  • shift-coupling
  • stable allocation
  • Stationary random measure


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