A Perron-Frobenius type result for integer maps and applications

TL;DR

This paper extends Perron-Frobenius theory to certain integer maps, demonstrating the existence of approximate eigenvectors, with applications in epidemiology and resource allocation.

Contribution

It introduces a Perron-Frobenius type result for concave maps on integer lattices, providing a new theoretical tool for discrete systems.

Findings

Approximate eigenvectors exist for certain integer maps.

Applications demonstrated in epidemiology and resource allocation.

Theoretical extension of Perron-Frobenius to discrete settings.

Abstract

It is shown that for certain maps, including concave maps, on the $d$-dimensional lattice of positive integer points, 'approximate' eigenvectors can be found. Applications in epidemiology as well as distributed resource allocation are discussed as examples.