On the time constant of high dimensional first passage percolation

Antonio Auffinger; Si Tang

doi:10.1214/16-EJP1

On the time constant of high dimensional first passage percolation

Antonio Auffinger, Si Tang

Mathematics

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

2 Scopus citations

Abstract

We study the time constant µ(e1) in first passage percolation on ℤ^d as a function of the dimension. We prove that if the passage times have finite mean, (equation found) where a ∈ [0,∞] is a constant that depends only on the behavior of the distribution of the passage times at 0. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a d-dimensional cube or diamond, provided that d is large enough.

Original language	English (US)
Journal	Electronic Journal of Probability
Volume	21
DOIs	https://doi.org/10.1214/16-EJP1
State	Published - 2016

Keywords

Eden model
First passage percolation
Limit shape
Time constant

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/16-EJP1

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abstract = "We study the time constant µ(e1) in first passage percolation on ℤd as a function of the dimension. We prove that if the passage times have finite mean, (equation found) where a ∈ [0,∞] is a constant that depends only on the behavior of the distribution of the passage times at 0. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a d-dimensional cube or diamond, provided that d is large enough.",

keywords = "Eden model, First passage percolation, Limit shape, Time constant",

author = "Antonio Auffinger and Si Tang",

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T1 - On the time constant of high dimensional first passage percolation

AU - Auffinger, Antonio

AU - Tang, Si

PY - 2016

Y1 - 2016

N2 - We study the time constant µ(e1) in first passage percolation on ℤd as a function of the dimension. We prove that if the passage times have finite mean, (equation found) where a ∈ [0,∞] is a constant that depends only on the behavior of the distribution of the passage times at 0. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a d-dimensional cube or diamond, provided that d is large enough.

AB - We study the time constant µ(e1) in first passage percolation on ℤd as a function of the dimension. We prove that if the passage times have finite mean, (equation found) where a ∈ [0,∞] is a constant that depends only on the behavior of the distribution of the passage times at 0. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a d-dimensional cube or diamond, provided that d is large enough.

KW - Eden model

KW - First passage percolation

KW - Limit shape

KW - Time constant

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DO - 10.1214/16-EJP1

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VL - 21

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

ER -

On the time constant of high dimensional first passage percolation

Abstract

Keywords

ASJC Scopus subject areas

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