Discrete hammersley's lines with sources and sinks

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

doi:10.30757/alea.v13-02

Discrete hammersley's lines with sources and sinks

A. L. Basdevant
, N. Enriquez
, L. Gerin
, J. B. Gouéré

Université Paris X
Université de Tours

Research output: Contribution to journal › Article › peer-review

Abstract

We consider 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.

Original language	English
Pages (from-to)	33-52
Number of pages	20
Journal	Alea (Rio de Janeiro)
Volume	13
Issue number	1
DOIs	https://doi.org/10.30757/alea.v13-02
Publication status	Published - 1 Jan 2016

Keywords

Hammersley's process
Longest increasing subsequences
Ulam's problem

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AU - Gerin, L.

AU - Gouéré, J. B.

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N2 - We consider 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.

AB - We consider 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.

KW - Hammersley's process

KW - Longest increasing subsequences

KW - Ulam's problem

U2 - 10.30757/alea.v13-02

DO - 10.30757/alea.v13-02

M3 - Article

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EP - 52

JO - Alea (Rio de Janeiro)

JF - Alea (Rio de Janeiro)

IS - 1

ER -

Discrete hammersley's lines with sources and sinks

Abstract

Keywords

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