Translator Disclaimer
2020 Optimal exponent for coalescence of finite geodesics in exponential last passage percolation
Lingfu Zhang
Electron. Commun. Probab. 25(none): 1-14 (2020). DOI: 10.1214/20-ECP354

Abstract

In this note, we study the model of directed last passage percolation on $\mathbb{Z} ^{2}$, with i.i.d. exponential weight. We consider the maximum directed paths from vertices $(0,\lfloor k^{2/3}\rfloor )$ and $(\lfloor k^{2/3} \rfloor ,0)$ to $(n,n)$, respectively. For the coalescence point of these paths, we show that the probability for it being $>Rk$ far away from the origin is in the order of $R^{-2/3}$. This is motivated by a recent work of Basu, Sarkar, and Sly [7], where the same estimate was obtained for semi-infinite geodesics, and the optimal exponent for the finite case was left open. Our arguments also apply to other exactly solvable models of last passage percolation.

Citation

Download Citation

Lingfu Zhang. "Optimal exponent for coalescence of finite geodesics in exponential last passage percolation." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP354

Information

Received: 18 March 2020; Accepted: 5 October 2020; Published: 2020
First available in Project Euclid: 22 October 2020

MathSciNet: MR4167385
Digital Object Identifier: 10.1214/20-ECP354

Subjects:
Primary: 60K35, 82C23

JOURNAL ARTICLE
14 PAGES


SHARE
Back to Top