The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Annales de l’Institut Henri Poincaré D


Full-Text PDF (650 KB) | Metadata | Table of Contents | AIHPD summary
Online access to the full text of Annales de l’Institut Henri Poincaré D is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 8, Issue 2, 2021, pp. 213–241
DOI: 10.4171/AIHPD/102

Published online: 2021-03-05

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. 8 (2021), 213-241. doi: 10.4171/AIHPD/102