Busemann functions and Equilibrium measures in last passage percolation models

Eric Cator; Leandro P. R. Pimentel

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arXiv · 0901.2450

Busemann functions and Equilibrium measures in last passage percolation models

Eric Cator·Leandro P. R. Pimentel

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Abstract

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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BibTeX RIS

Eric Cator, Leandro P. R. Pimentel. 2010-01-26. Busemann functions and Equilibrium measures in last passage percolation models. https://arxiv.org/abs/0901.2450

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