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Tertiles and the time constant

Part of: Limit theorems Special processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  16 July 2020

Daniel Ahlberg Open the ORCID record for Daniel Ahlberg [Opens in a new window]
Daniel Ahlberg*
Affiliation:
Stockholm University
*
*Postal address: Department of Mathematics, Stockholm University, SE - 106 91 Stockholm, Sweden. Email address: daniel.ahlberg@math.su.se
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Abstract

We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence, we obtain a counter-example to a problem proposed by Alm and Deijfen (2015).

Keywords

First-passage percolationquantilestime constant

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60F15: Strong theorems 82B43: Percolation
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 407 - 408
Copyright
© Applied Probability Trust 2020

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References

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