, Volume 23, Issue 3, pp 545–570 | Cite as

A Perron–Frobenius type result for integer maps and applications

  • Ohad GiladiEmail author
  • Björn S. Rüffer


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.


Perron–Frobenius theory Integer maps Concave maps Hilbert metric 

Mathematics Subject Classification

37J25 92D30 93D20 



This paper was written while both authors were members of the ‘priority research centre for Computer-Assisted Research Mathematics and its Applications’ (CARMA) at the University of Newcastle, Australia (UON). CARMA was founded in 2009 by Jonathan M. Borwein, who also served as its director. Jon was a prolific researcher and a devoted friend. This paper is dedicated to his memory with admiration.


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Authors and Affiliations

  1. 1.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia

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