A shape theorem and semi-infinite geodesics for the Hammersley model with random weights

作者：Cator Eric^*; Pimentel Leandro P R

来源：Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2011, 8: 163-175.

• Last-passage percolation
• Hammersley model
• shape theorem
• semi-infinite geodesics

In this paper we will prove a shape theorem for the last-passage percolation model on a two dimensional F-compound Poisson process, called the Hammersley model with random weights. We will also provide diffusive upper bounds for shape fluctuations. Finally we will indicate how these results can be used to prove existence and coalescence of semi-infinite geodesics in some fixed direction alpha, following an approach developed by Newman and co-authors Howard and Newman (2001); Licea and Newman (1996); Newman (1995), and applied to the classical Hammersley process by Wuthrich in Wuthrich (2002). These results will be crucial in the development of an upcoming paper on the relation between Busemann functions and equilibrium measures in last-passage percolation models Cator and Pimentel (2009).

• 出版日期2011