Geodesics in two-dimensional first-passage percolation

Cristina Licea; Charles M. Newman

doi:10.1214/aop/1042644722

Geodesics in two-dimensional first-passage percolation

Cristina Licea, Charles M. Newman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider standard first-passage percolation on ℤ₂. Geodesics are nearest-neighbor paths in ℤ², each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.

Original language	English (US)
Pages (from-to)	399-410
Number of pages	12
Journal	Annals of Probability
Volume	24
Issue number	1
DOIs	https://doi.org/10.1214/aop/1042644722
State	Published - 1996

Keywords

Disordered Ising model
First-passage percolation
Geodesic
Random metric

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/aop/1042644722

Cite this

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abstract = "We consider standard first-passage percolation on ℤ2. Geodesics are nearest-neighbor paths in ℤ2, each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.",

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AU - Newman, Charles M.

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AB - We consider standard first-passage percolation on ℤ2. Geodesics are nearest-neighbor paths in ℤ2, each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.

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KW - First-passage percolation

KW - Geodesic

KW - Random metric

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Geodesics in two-dimensional first-passage percolation

Abstract

Keywords

ASJC Scopus subject areas

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