Busemann functions and Equilibrium measures in last passage percolation models

Details Busemann functions and Equilibrium measures in last passage percolation models Busemann functions and Equilibrium measures in last passage percolation models

2009-01-16

arxiv.org/abs/0901.2450v3

Mathematics

Probability

23 pages 3rd. version: major revision, some new results

Scientific paper

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.

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