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Probability Theory and Related Fields

, Volume 154, Issue 1–2, pp 89–125

First Online: 11 April 2011Received: 10 December 2010Revised: 28 March 2011


The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium or time-invariant measures for the related multi-class interacting fluid system. As we shall see, in the classical Hammersley model, where each point has weight one, this approach brings a new and rather geometrical solution of the longest increasing subsequence problem, as well as a central limit theorem for the Busemann function.

KeywordsHammersley process Last passage percolation Busemann functions Equilibrium L. P. R. Pimentel was supported by grant number 613.000.605 from the Netherlands Organisation for Scientific Research NWO.

Mathematics Subject Classification 2000Primary 60C05 60K35 Secondary 60F05  Download to read the full article text

Author: Eric Cator - Leandro P. R. Pimentel

Source: https://link.springer.com/

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