Annales de l’Institut Henri Poincaré D


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Published online first: 2021-03-05
DOI: 10.4171/AIHPD/102

Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints

Niccolò Torri[1] and Quentin Berger[2]

(1) Université Paris Nanterre, France
(2) Sorbonne Université, Paris, France

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 $\mathcal L_m$ 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 $\mathcal L_m$ in a general manner, and we illustrate the interest and usefulness of this generalized LPP with examples and simulations.

Keywords: Last-passage percolation, polymer models, non-directed polymers

Torri Niccolò, Berger Quentin: Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints. Ann. Inst. Henri Poincaré Comb. Phys. Interact. Electronically published on March 5, 2021. doi: 10.4171/AIHPD/102 (to appear in print)