Classification of the limit shape for 1+1-dimensional FPP

Fuente: arXiv
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Autore principale: Hassler, Malte
Natura: Preprint
Pubblicazione: 2024
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_version_ 1866913806866710528
author Hassler, Malte
author_facet Hassler, Malte
contents We introduce a simplified model of planar first passage percolation where weights along vertical edges are deterministic. We show that the limit shape has a flat edge in the vertical direction if and only if the random distribution of the horizontal edges has an atom at the infimum of its support. Furthermore, we present bounds on the upper and lower derivative of the time constant.
format Preprint
id arxiv_https___arxiv_org_abs_2411_13030
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Classification of the limit shape for 1+1-dimensional FPP
Hassler, Malte
Probability
60K35, 60K37, 82B43
We introduce a simplified model of planar first passage percolation where weights along vertical edges are deterministic. We show that the limit shape has a flat edge in the vertical direction if and only if the random distribution of the horizontal edges has an atom at the infimum of its support. Furthermore, we present bounds on the upper and lower derivative of the time constant.
title Classification of the limit shape for 1+1-dimensional FPP
topic Probability
60K35, 60K37, 82B43
url https://arxiv.org/abs/2411.13030