Open Access
2020 Coalescence estimates for the corner growth model with exponential weights
Timo Seppäläinen, Xiao Shen
Electron. J. Probab. 25: 1-31 (2020). DOI: 10.1214/20-EJP489


We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent $3/2$. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have matching optimal exponential order of magnitude. For slow coalescence we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor.


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Timo Seppäläinen. Xiao Shen. "Coalescence estimates for the corner growth model with exponential weights." Electron. J. Probab. 25 1 - 31, 2020.


Received: 27 November 2019; Accepted: 27 June 2020; Published: 2020
First available in Project Euclid: 22 July 2020

zbMATH: 07252717
MathSciNet: MR4125790
Digital Object Identifier: 10.1214/20-EJP489

Primary: 60K35 , 60K37

Keywords: coalescence exit time , fluctuation exponent , Geodesic , Kardar-Parisi-Zhang , Last-passage percolation , random growth model

Vol.25 • 2020
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