Water transport on infinite graphs


  • Author: Statistics Views
  • Date: 27 May 2019

Each week, we select a recently published article and offer either free access or highlight a recent open access publication. This week's is from Random Structures and Algorithms and is available from the May 2019 issue.

Water transport on infinite graphs

Olle Häggström and Timo Hirscher

Random Structures and Algorithms, Volume 54, Issue 3,May 2019, pages 515-527

DOI: https://doi.org/10.1002/rsa.20801

thumbnail image: Water transport on infinite graphs

If the nodes of a graph are considered to be identical barrels – featuring different water levels – and the edges to be (locked) water‐filled pipes in between the barrels, consider the optimization problem of how much the water level in a fixed barrel can be raised with no pumps available, that is, by opening and closing the locks in an elaborate succession. This model is related to an opinion formation process, the so‐called Deffuant model. We consider the initial water profile to be given by i.i.d. unif(0,1) random variables, investigate the supremum of achievable water levels at a given node – or to be more precise, the support of its distribution – and ask in which settings it becomes degenerate, that is, reduces to a single value. This turns out to be the case for all infinite connected quasi‐transitive graphs, with exactly one exception: the two‐sided infinite path.

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