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Journal Articles Journal of Theoretical Probability Year : 2016

A Cut-Invariant Law of Large Numbers for Random Heaps

Samy Abbes

Abstract

Heap monoids equipped with Bernoulli measures are a model of probabilistic asynchronous systems. We introduce in this framework the notion of asynchronous stopping time, which is analogous to the notion of stopping time for classical probabilistic processes. A Strong Bernoulli property is proved. A notion of cut-invariance is formulated for convergent ergodic means. Then a version of the Strong law of large numbers is proved for heap monoids with Bernoulli measures. Finally, we study a sub-additive version of the Law of large numbers in this framework based on Kingman sub-additive Ergodic Theorem.

Dates and versions

hal-01328460 , version 1 (08-06-2016)

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Samy Abbes. A Cut-Invariant Law of Large Numbers for Random Heaps. Journal of Theoretical Probability, 2016, pp.29. ⟨10.1007/s10959-016-0692-6⟩. ⟨hal-01328460⟩
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