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Non-existence of bi-infinite geodesics in the exponential corner growth model

Part of: Special processes

Published online by Cambridge University Press:  16 November 2020

Márton Balázs ,
Ofer Busani  and
Timo Seppäläinen
Márton Balázs
Affiliation:
University of Bristol, School of Mathematics, Fry Building, Woodland Rd., BristolBS8 1UG, UK, E-mail: m.balazs@bristol.ac.uk; https://people.maths.bris.ac.uk/~mb13434/
Ofer Busani
Affiliation:
University of Bristol, School of Mathematics, Fry Building, Woodland Rd., BristolBS8 1UG, UK, E-mail: o.busani@bristol.ac.uk; https://people.maths.bris.ac.uk/~di18476/
Timo Seppäläinen
Affiliation:
University of Wisconsin-Madison, Mathematics Department, Van Vleck Hall, 480 Lincoln Dr., Madison, WI 53706-1388, USA, E-mail: seppalai@math.wisc.edu; http://www.math.wisc.edu/~seppalai

Abstract

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This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

Keywords

bi-infinitecorner growth modeldirected percolationgeodesicrandom growth modellast-passage percolationqueues

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60K37: Processes in random environments
Type
Probability
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e46
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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