2022
DOI: 10.1112/jlms.12639
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A non‐conservative Harris ergodic theorem

Abstract: We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides quantitative estimates of the spectral gap, complementing Krein-Rutman theorems and generalizing probabilistic approaches. The proof is based on a non-homogenous ℎ-transform of the semigroup and the construction of Lyapunov functions for this latter. It exploits then the classical nec… Show more

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Cited by 19 publications
(27 citation statements)
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“…Finally, note that the theorems from [28] and [7] on which our existence and longterm convergence results hinge are very general and would allow us to consider various generalisations of our type-dependent growth and fragmentation mechanisms. However, in the particular case considered here all the quantities and functions of interest are explicit (a nice property which is bound to fail for most generalisations) and in future work we intend to apply this precise model to experimental data, in collaboration with our colleagues from the NEMATIC 1 research project.…”
Section: Introductionmentioning
confidence: 93%
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“…Finally, note that the theorems from [28] and [7] on which our existence and longterm convergence results hinge are very general and would allow us to consider various generalisations of our type-dependent growth and fragmentation mechanisms. However, in the particular case considered here all the quantities and functions of interest are explicit (a nice property which is bound to fail for most generalisations) and in future work we intend to apply this precise model to experimental data, in collaboration with our colleagues from the NEMATIC 1 research project.…”
Section: Introductionmentioning
confidence: 93%
“…Before we present this result, we need some notational preparation. The approach we shall adopt is the semigroup approach of [7].…”
Section: Convergence Of the Mean Measurementioning
confidence: 99%
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