2009/01/16 by Eric Cator, Cator, Eric, Leandro P. R. Pimentel +1
Mathematics · Physics and Astronomy · #60C05 #60F05 (Secondary) #60K35 (Primary) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.0901.2450
openalex publication_date 2009/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The interplay between two-dimensional percolation growth models and\none-dimensional particle processes has been a fruitful source of interesting\nmathematical phenomena. In this paper we develop a connection between the\nconstruction of Busemann functions in the Hammersley last-passage percolation\nmodel with i.i.d. random weights, and the existence, ergodicity and uniqueness\nof equilibrium (or time-invariant) measures for the related (multi-class)\ninteracting fluid system. As we shall see, in the classical Hammersley model,\nwhere each point has weight one, this approach brings a new and rather\ngeometrical solution of the longest increasing subsequence problem, as well as\na central limit theorem for the Busemann function.\n