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

Marton Balazs; Ofer Busani; Timo Seppäläinen

doi:10.1017/fms.2020.31

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

Marton Balazs
, Ofer Busani^*
, Timo Seppäläinen

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

29 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	E46
Number of pages	32
Journal	Forum of Mathematics, Sigma
Volume	8
DOIs	https://doi.org/10.1017/fms.2020.31
Publication status	Published - 16 Nov 2020

Keywords

bi-infinite, corner growth model, directed percolation, geodesic, random growth model, last-passage percolation, queues

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10.1017/fms.2020.31

https://arxiv.org/abs/1909.06883

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title = "Non-existence of bi-infinite geodesics in the exponential corner growth model",

abstract = "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-infinite, corner growth model, directed percolation, geodesic, random growth model, last-passage percolation, queues",

author = "Marton Balazs and Ofer Busani and Timo Sepp{\"a}l{\"a}inen",

year = "2020",

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AU - Balazs, Marton

AU - Busani, Ofer

AU - Seppäläinen, Timo

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Y1 - 2020/11/16

N2 - 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.

AB - 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.

KW - bi-infinite, corner growth model, directed percolation, geodesic, random growth model, last-passage percolation, queues

UR - https://arxiv.org/abs/1909.06883

U2 - 10.1017/fms.2020.31

DO - 10.1017/fms.2020.31

M3 - Article (Academic Journal)

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VL - 8

SP - E46

JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

ER -

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

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Stochastic interacting systems: connections, fluctuations and applications

Professor Marton Balazs

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

Abstract

Keywords

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Stochastic interacting systems: connections, fluctuations and applications

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Professor Marton Balazs

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