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A Cut-Invariant Law of Large Numbers for Random Heaps

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.
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https://hal.inria.fr/hal-01328460
Contributor : Samy Abbes <>
Submitted on : Wednesday, June 8, 2016 - 9:37:51 AM
Last modification on : Saturday, April 11, 2020 - 2:12:53 AM

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

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