Geodesic forests in last-passage percolation

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• 作者：Sergio I. Ló ; pez^a ; ^{silo@ciencias.unam.mx} ; Leandro P.R. Pimentel^b ; ^{leandro@im.ufrj.br} ; ^{lprpimentel@gmail.com}
• 关键词：Last-passage percolation ; Geodesic forest ; Competition interface ; Airy process
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：304-324
• 全文大小：633 K
• 卷排序：127

文摘

The aim of this article is to study the forest composed by point-to-line geodesics in the last-passage percolation model with exponential weights. We will show that the location of the root can be described in terms of the maxima of a random walk, whose distribution will depend on the geometry of the substrate (line). For flat substrates, we will get power law behaviour of the height function, study its scaling limit, and describe it in terms of variational problems involving the Airy process.