Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints
Niccolò Torri
Université Paris Nanterre, FranceQuentin Berger
Sorbonne Université, Paris, France
Abstract
Hammersley’s Last-Passage Percolation (LPP), also known as Ulam’s problem, is a well-studied model that can be described as follows: let points be chosen uniformly and independently in [0,1], then what is the maximal number 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 in a general manner, and we illustrate the interest and usefulness of this generalized LPP with examples and simulations.
Cite this article
Niccolò Torri, Quentin Berger, Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 8 (2021), no. 2, pp. 213–241
DOI 10.4171/AIHPD/102