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September 2020 On the number of maximal paths in directed last-passage percolation
Hugo Duminil-Copin, Harry Kesten, Fedor Nazarov, Yuval Peres, Vladas Sidoravicius
Ann. Probab. 48(5): 2176-2188 (September 2020). DOI: 10.1214/19-AOP1419

Abstract

We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ${\mathbb{Z}}^{d}$ $(d\geq 2)$ in which weights take finitely many values is typically exponentially large.

Citation

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Hugo Duminil-Copin. Harry Kesten. Fedor Nazarov. Yuval Peres. Vladas Sidoravicius. "On the number of maximal paths in directed last-passage percolation." Ann. Probab. 48 (5) 2176 - 2188, September 2020. https://doi.org/10.1214/19-AOP1419

Information

Received: 1 June 2018; Revised: 1 November 2019; Published: September 2020
First available in Project Euclid: 23 September 2020

MathSciNet: MR4152639
Digital Object Identifier: 10.1214/19-AOP1419

Subjects:
Primary: 60C05

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 5 • September 2020
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