Discrete Hammersley's Lines with sources and sinks
Probability
2015-04-08 v2
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. Sepp{\"a}l{\"a}inen 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.
Cite
@article{arxiv.1503.00507,
title = {Discrete Hammersley's Lines with sources and sinks},
author = {A. -L. Basdevant and N. Enriquez and L. Gerin and J. -B. Gouéré},
journal= {arXiv preprint arXiv:1503.00507},
year = {2015}
}