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abstract: |
    Understanding how knowledge is created and propagates within groups is crucial to explain how human populations have evolved through time. Anthropologists have relied on different theoretical models to address this question. In this work, we introduce a mathematically oriented model that shares properties with individual based approaches, inhomogeneous Markov chains and learning algorithms, such as those introduced in \[F. Cucker, S. Smale, *Bull. Amer. Math. Soc*, 39 (1), 2002\] and \[F. Cucker, S. Smale and D. X Zhou, *Found. Comput. Math.*, 2004\]. After deriving the model, we study some of its mathematical properties, and establish theoretical and quantitative results in a simplified case. Finally, we run numerical simulations to illustrate some properties of the model.\
    <span style="font-variant:small-caps;">Keywords:</span> Individual based model, inhomogeneous Markov chains, convergence to equilibrium, numerical simulations, concentration inequalities, cultural evolution, language evolution, cumulative culture.\
    <span style="font-variant:small-caps;">2010 Mathematics Subject Classification:</span> 92D25, 68T05, 92H10.
address:
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    Univ. Lille, CNRS, UMR 8198 - Evo-Eco-Paleo, F-59000 Lille, France\
    Email: `sylvain.billiard@univ-lille.fr`
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    Institute for Advanced Study in Toulouse, CNRS, UMR 5314\
    F-31015 Toulouse, France\
    Email: `maxime.derex@iast.fr`
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    National Museum of Natural History, UMR 7205, Institut de Systématique, Evolution et Biodiversité\
    F-75005 Paris, France\
    Email: 