ON THE NUMBER OF MAXIMAL PATHS IN DIRECTED LAST-PASSAGE PERCOLATION

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

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Bibliographic Details
Published in:The Annals of probability 2020-09, Vol.48 (5), p.2176-2188
Main Authors: Duminil-Copin, Hugo, Kesten, Harry, Nazarov, Fedor, Peres, Yuval, Sidoravicius, Vladas
Format: Article
Language:English
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Summary:We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ℤ d (d ≥ 2) in which weights take finitely many values is typically exponentially large.
ISSN:0091-1798
2168-894X
DOI:10.1214/19-aop1419