Beyond Hammersley’s Last-Passage Percolation: a discussion on possible local and global constraints
Quentin Berger, Niccolò Torri
Source 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 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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.