Discrete Hammersley's Lines with sources and sinks

A-L Basdevant; N Enriquez; L Gerin; J-B Gouéré

Discrete Hammersley's Lines with sources and sinks

A-L Basdevant ¹ N Enriquez ^{2, 1} L Gerin ³ J-B Gouéré ⁴

1 MODAL'X - Modélisation aléatoire de Paris X

2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

4 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Keywords : Ulam's problem Hammersley's process longest increasing subsequences

Document type :

Journal articles

Domain :

Mathematics [math] / Probability [math.PR]

Mathematics [math] / Combinatorics [math.CO]

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https://hal.archives-ouvertes.fr/hal-01121585
Contributor : Lucas Gerin <>
Submitted on : Thursday, April 2, 2015 - 11:32:49 AM
Last modification on : Thursday, April 4, 2019 - 1:27:37 AM
Document(s) archivé(s) le : Tuesday, April 18, 2017 - 9:01:10 AM

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Discrete Hammersley's Lines with sources and sinks

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