Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints
Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 2, pp. 213-241.
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Hammersley’s Last-Passage Percolation (LPP), also known as Ulam’s problem, is a well-studied model that can be described as follows: let m points be chosen uniformly and independently in [0,1] 2 , then what is the maximal number ℒ m of points that can be collected by an up-right path? We introduce here a generalization of this LPP, allowing for more general constraints than the up-right condition: the constraints may be either local or global. We give the correct order of ℒ m in a general manner, and we illustrate the interest and usefulness of this generalized LPP with examples and simulations.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/102
Classification : 60-XX, 82-XX
Mots-clés : Last-passage percolation, polymer models, non-directed polymers 
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Berger, Quentin; Torri, Niccolò. Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 2, pp. 213-241. doi : 10.4171/aihpd/102. http://archive.numdam.org/articles/10.4171/aihpd/102/

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