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2011.69: Stochastic production trees as products of i.i.d. componentwise exponential max-plus matrices

2011.69: James Hook and Dave Broomhead (2011) Stochastic production trees as products of i.i.d. componentwise exponential max-plus matrices.

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Abstract

We introduce a class of stochastic production tree model, based on Petri nets, which admit a random matrix product description in the Max-plus algebra. With a kind of combinatorial change of variables we are able to simplify the form of the matrices arising from these models. For this class of \emph{Componentwise exponential} matrix we prove a new result relating the (Max-plus) spectrum of the product to the principal (classical) eigenvalue of an associated adjacency matrix by means of a sandwich inequality. This theorem highlights several important theoretical factors in the dynamics of Max-plus linear systems generally and gives us some neat insight into the different production tree models.

Item Type:MIMS Preprint
Uncontrolled Keywords:Max-plus algebra, tropical algebra, queues, petri-nets, random matrices, extreme value statistic
Subjects:MSC 2000 > 05 Combinatorics
MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 62 Statistics
MSC 2000 > 92 Biology and other natural sciences
MSC 2000 > 94 Information and communication, circuits
MIMS number:2011.69
Deposited By:Mr James Hook
Deposited On:18 August 2011

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