On the number of maximal paths in directed last-passage percolation

TL;DR

This paper demonstrates that in directed last-passage percolation on hypercubic lattices with finitely many weights, the number of maximal paths is generally exponentially large, highlighting complexity in such models.

Contribution

It establishes the typical exponential growth in the number of maximal paths in directed last-passage percolation with finitely many weights.

Findings

Number of maximal paths is typically exponentially large.

Results apply to hypercubic lattices in dimensions d ≥ 2.

Highlights complexity in last-passage percolation models.

Abstract

We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ${\mathbb Z}^d$ $(d\geq2)$ in which weights take finitely many values is typically exponentially large.