Geodesic Forests in the Last-Passage Percolation
Probability
2015-10-07 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1510.01552,
title = {Geodesic Forests in the Last-Passage Percolation},
author = {Sergio I. Lopez and Leandro P. R. Pimentel},
journal= {arXiv preprint arXiv:1510.01552},
year = {2015}
}
Comments
20 pages