Type of Document Master's Thesis Author Farlow, Kasie Geralyn Author's Email Address kfar1228@vt.edu URN etd-05042009-152934 Title Max-Plus Algebra Degree Master of Science Department Mathematics Advisory Committee

Advisor Name Title Day, Martin V. Committee Chair Haskell, Peter E. Committee Member Wheeler, Robert L. Committee Member Keywords

- Markov Chains
- Linear Algebra
- Max-Plus
Date of Defense 2009-04-27 Availability unrestricted AbstractIn max-plus algebra we work with the max-plus semi-ring which is the set R_{max}=[-infinity,infinity) together with operations "a+b"=max(a,b) and "ab"= a +b. The additive and multiplicative identities are taken to beepsilon=-infinity and e=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various

fieldsof mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as

in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear. Max-plus

algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear

algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence.Files

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