January 2022 Universality of the geodesic tree in last passage percolation
Ofer Busani, Patrik L. Ferrari
Author Affiliations +
Ann. Probab. 50(1): 90-130 (January 2022). DOI: 10.1214/21-AOP1530


In this paper, we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder located around the point (N,N), and whose width and length are o(N2/3) and o(N), respectively, agrees in the cylinder, with the stationary geodesic sharing the same end-point. In the case of the point-to-point model where the geodesic starts from the origin, we consider width δN2/3, length up to δ3/2N/(log(δ1))3, and provide lower and upper bounds for the probability that the geodesics agree in that cylinder.

Funding Statement

O. Busani was supported by the EPSRC EP/R021449/1 Standard Grant of the UK. This study did not involve any underlying data. The work of P.L. Ferrari was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—GZ 2047/1, projekt-id 390685813 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Projektnummer 211504053—SFB 1060.


The authors are grateful to Márton Balázs for initial discussions on the topic that led to our collaboration. We are also very grateful to an anonymous referee for careful reading and a number of constructive remarks.


Download Citation

Ofer Busani. Patrik L. Ferrari. "Universality of the geodesic tree in last passage percolation." Ann. Probab. 50 (1) 90 - 130, January 2022. https://doi.org/10.1214/21-AOP1530


Received: 1 August 2020; Revised: 1 March 2021; Published: January 2022
First available in Project Euclid: 23 February 2022

MathSciNet: MR4385124
zbMATH: 1499.60325
Digital Object Identifier: 10.1214/21-AOP1530

Primary: 60K35 , 60K37

Keywords: coalescence of geodesics , geodesics , Kardar–Parisi–Zhang universality , Last passage percolation , Polymers

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 1 • January 2022
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