A shape theorem and semi-infinite geodesics for the Hammersley model with random weights
A shape theorem and semi-infinite geodesics for the Hammersley model with random weights
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随机权重 Hammersley 模型的形状定理和半无限测地线
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Leandro P. R. Pimentel
中科院分区：
文献类型：
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作者：
E. Cator;Leandro P. R. Pimentel
本文证明了二维$F~-复合泊松过程的最后一次渗流模型的一个形状定理，称为随机权Hammersley模型。我们还将提供形状波动的扩散上限。最后，我们将说明这些结果如何用来证明在某个固定方向上半无限测地线的存在和合并，遵循Newman和合著者提出的方法，并将其应用于Wuthrich的经典Hammersley过程。这些结果将对即将发表的关于Busemann函数与最后一段渗流模型中的平衡度量之间的关系的论文的发展至关重要。
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, and applied to the classical Hammersley process by W\"uthrich. 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.