Print Email Facebook Twitter Busemann functions and equilibrium measures in last passage percolation models Title Busemann functions and equilibrium measures in last passage percolation models Author Cator, E. Pimentel, L.P.R. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2011-04-11 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 timeinvariant) 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. Subject Hammersley processLast passage percolationBusemann functionsEquilibrium To reference this document use: http://resolver.tudelft.nl/uuid:335a8f1a-5af7-4143-af1e-208f44526ba6 DOI https://doi.org/10.1007/s00440-011-0363-6 Publisher Springer Verlag ISSN 0178-8051 Source Probability Theory and Related Fields, 2011 Part of collection Institutional Repository Document type journal article Rights (c) 2011 Cator, E.Pimentel, L.P.R.This article is published with open access at Springerlink.com Files PDF cator2010.pdf 454.43 KB Close viewer /islandora/object/uuid:335a8f1a-5af7-4143-af1e-208f44526ba6/datastream/OBJ/view