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Discrete Hammersley's Lines with sources and sinks

Abstract : We introduce two stationary versions of two discrete variants of Hammersley's process in a finite box, this allows us to recover in a unified and simple way the laws of large numbers proved by T. Seppäläinen for two generalized Ulam's problems. As a by-product we obtain an elementary solution for the original Ulam problem. We also prove that for the first process defined on Z, Bernoulli product measures are the only extremal and translation-invariant stationary measures.
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Contributor : Lucas Gerin Connect in order to contact the contributor
Submitted on : Thursday, April 2, 2015 - 11:32:49 AM
Last modification on : Tuesday, November 16, 2021 - 4:51:39 AM
Long-term archiving on: : Tuesday, April 18, 2017 - 9:01:10 AM


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  • HAL Id : hal-01121585, version 2
  • ARXIV : 1503.00507


A-L Basdevant, N Enriquez, L Gerin, J-B Gouéré. Discrete Hammersley's Lines with sources and sinks. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2016, 13 (1), pp.33-52. ⟨hal-01121585v2⟩



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